WASHINGTON — A trade dispute over Canadian lumber that began when Ronald Reagan was president has become a political problem for President Biden, with home builders and members of Congress urging the administration to try to strike a deal that could help bring down the cost of critical building materials.Lumber prices remain far above prepandemic levels, even after falling sharply in recent weeks, an increase driven in part by strong housing demand and an abundance of home improvement projects during the pandemic. The higher-than-normal prices are among a wide range of supply chain complications that have cropped up as the economy picks up steam.But unlike other commodities that have been in short supply, lumber is also the subject of a long-running trade dispute between the United States and Canada, adding a layer of diplomatic intrigue to the scramble for in-demand building materials. The two countries are locked in a thorny disagreement over softwood lumber, which is widely used to build single-family homes.In the latest chapter of the dispute, the Trump administration in 2017 imposed duties on Canadian softwood lumber imports in response to what it deemed unfair trade practices. Now, with lumber prices driving up the cost of new home construction, the Biden administration is facing pressure to seek a resolution to the long-running spat.“If you look at the structure of home building — a lot of wood there,” said Representative Brian Higgins, Democrat of New York, whose Buffalo-area district borders Canada. “So the cost of softwood lumber is going to profoundly influence the cost that is inevitably passed on to the consumer.”The National Association of Home Builders, an influential trade group, has been particularly vocal about the issue, and numerous lawmakers have taken an interest as well. Last month, a bipartisan group of nearly 100 House members, led by Mr. Higgins and Representative Kevin Hern, Republican of Oklahoma, wrote to Katherine Tai, the United States trade representative, urging her to seek a deal with Canada.But signs of diplomatic progress have been scarce, and Canadian lumber producers may soon face higher duties. The Commerce Department said last month that it tentatively planned to double the duties later this year, to 18.3 percent from 9 percent for most producers.The move was cheered by the American lumber industry, but it drew criticism from U.S. home builders along with the Canadian government and the country’s lumber industry. Chuck Fowke, a custom home builder in Florida and the chairman of the National Association of Home Builders, said the planned increase “shows the White House does not care about the plight of American home buyers and renters.”Commerce Secretary Gina Raimondo, who met with the home builders group last month, said afterward that she would seek to “identify targeted actions the government or industry can take to address supply chain constraints.”Finding a resolution to the trade dispute is unlikely to be a simple undertaking for the Biden administration. “There’s really nothing that the administration can do quickly,” said Scott Lincicome, a senior fellow at the libertarian Cato Institute, who criticized the lumber duties and the system that allows domestic industries to seek them.The United States and Canada have been at odds over lumber since the 1980s. The saga has gone on for so long that lumber disputes over the years are commonly referred to with Roman numerals, akin to the Super Bowl. The current dispute is called Lumber V; Lumber IV took place during the George W. Bush administration.The friction between the United States and Canada over softwood lumber stems in large part from the differences in how timber is harvested in the two countries. While most timberland in the United States is privately owned, most of Canada’s forestland is publicly owned, and companies pay fees set by provincial governments to harvest timber from their land.A lumberyard in Victoria, British Columbia. Canadian lumber producers may soon face higher duties. James MacDonald/BloombergA sawmill in Chemainus, British Columbia. The U.S. Commerce Department said it tentatively planned to double the duties this year to 18.3 percent for most Canadian producers.James MacDonald/BloombergAmerican lumber producers contend that the fees are artificially low and amount to an unfair government subsidy. The United States and Canada have reached a series of agreements over the years regarding lumber imports into the United States, but the most recent deal expired in 2015.“The core problem, and partly why you can never resolve this, comes down to structure,” said Eric Miller, a former Canadian official and the president of the Rideau Potomac Strategy Group, a consultancy.In 2016, toward the end of the Obama administration, the American lumber industry petitioned the government to impose duties on Canadian softwood lumber imports in response to what it contended were unfair trade practices. The proceedings continued under the Trump administration, which in 2017 imposed duties of 20.2 percent for most Canadian producers. The rate was lowered to 9 percent last year.The status of the long-running dispute took on a new urgency as the price of lumber soared over the past year. The National Association of Home Builders estimated in April that higher lumber costs had added nearly $36,000 to the price of an average newly constructed single-family home. A benchmark for the price of framing lumber set a record high of $1,515 per thousand board feet in May, four times the price at the beginning of 2020, before beginning to plummet. Last week, the price stood at $930, still more than double its level at the start of 2020, according to Fastmarkets Random Lengths, the trade publication that publishes the benchmark.“As an economist, it is very hard to understand why we’re taxing something we don’t produce enough of,” said Robert Dietz, the chief economist for the National Association of Home Builders.On the other side of the issue are U.S. lumber producers. The U.S. Lumber Coalition, an industry group, has argued that strong demand, not duties, is driving lumber prices and that the duties make up only a small portion of the total cost of lumber for new homes.The coalition credits the duties with strengthening the U.S. lumber industry, saying in a statement that American sawmills had expanded capacity in recent years, producing an additional 11 billion board feet of lumber since 2016. “More lumber being manufactured in America to meet domestic demand is a direct result of the trade enforcement, and the U.S. industry strongly urges the administration to continue this enforcement,” the coalition said.Dustin Jalbert, a senior economist at Fastmarkets, a price reporting firm, attributed the chaotic lumber market and high prices in large part to effects from the pandemic. At the start of the pandemic, he said, sawmills “assumed the worst” and curbed production, only for the housing market to rebound and for demand to soar.Mr. Jalbert said the duties stemming from the U.S.-Canada dispute were not a major reason for the high prices. “In terms of the short-term pricing situation, it’s lower down the list in terms of the factors that are driving the record prices that we’ve seen in the market,” he said.Mr. Dietz of the home builders association acknowledged in an interview last month that “you could suspend the lumber tariff and you’re still not going to cool off this market,” adding, “A lot of the driving forces are on the demand side.”The National Association of Home Builders, a trade group, estimated in April that higher lumber costs had added nearly $36,000 to the price of an average newly constructed single-family home.Wes Frazer for The New York TimesThe status of the long-running dispute took on a new urgency as the price of lumber soared over the past year.Wes Frazer for The New York TimesBut he argued that getting rid of the duties would still be a useful step. “This is not a moment where we need to be saying: ‘Well, that’s going to help, but it’s not going to solve the problem. Therefore, it’s not a solution,’” he said.Even if the lumber duties are playing only a modest role in the current market conditions, the issue has still grabbed the attention of lawmakers. Ms. Tai and Ms. Raimondo both faced questions about lumber during hearings on Capitol Hill this spring.“The home builders, the Realtors, everybody in my state is talking about the cost of lumber,” Senator John Thune of South Dakota, the No. 2 Senate Republican, told Ms. Tai last month.Ms. Tai seemed to fault Canada for the stalemate. “In order to have an agreement and in order to have a negotiation, you need to have a partner,” she told Mr. Thune. “And thus far, the Canadians have not expressed interest in engaging.”Adam Hodge, a spokesman for Ms. Tai, said the United States was “open to resolving our differences” with Canada over softwood lumber. But, he added, “That would require addressing Canadian policies that create an uneven playing field for the U.S. industry, and to date, Canada has been unwilling to adequately address these concerns.”A spokeswoman for Mary Ng, the Canadian international trade minister, offered a different take on the Canadians’ interest in engaging on the issue.“Minister Ng has raised the United States’ unfair and unwarranted duties on softwood lumber at every opportunity, including directly with the president, with Secretary Raimondo and with Ambassador Tai, and we welcome discussions,” the spokeswoman, Alice Hansen, said. Prime Minister Justin Trudeau also raised the matter with Mr. Biden on the sidelines of the Group of 7 summit in Britain this month, Ms. Hansen said.At a recent parliamentary hearing, Ms. Ng described the duties as “a tax on the American people” that makes housing more expensive for them.“We do believe that a negotiated settlement would be in the best interest of both countries,” she said. “But in the meantime, we must defend against these unwarranted tariffs, which we will continue to do.” More