The U.S. government is facing increasing pressure to reach a deal with Canada on softwood lumber, as demand for construction materials is expected to spike higher in Texas and Florida in the wake of hurricanes Harvey and Irma.

While the U.S. lumber industry is dug in on its demand for tariffs, its customers argue that domestic supplies cannot meet their needs, which will drive up the cost of reconstruction in the states that sustained many billions of dollars in storm damage in recent weeks.

The Canadian government is hoping the added domestic pressure resulting from the hurricanes will help pave the way for a deal, Natural Resources Minister Jim Carr said on Thursday.

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"We know that [the looming reconstruction] has an influence on markets and on demand," Mr. Carr said after speaking at the Council of Forestry Ministers meeting in Ottawa.

"And we also know that Canadian producers offer a very good supply of softwood lumber in the United States. That's an economic reality. Market forces are important, so we think that will almost certainly have some impact on thinking."

However, during a visit to Washington on Thursday, Ontario Premier Kathleen Wynne said that a resolution to the softwood stand-off currently looks unlikely.

Ms. Wynne met with U.S. Commerce Secretary Wilbur Ross at his office in Washington.

"He didn't hold out, I would say, a clear hope that there is an easy resolution on the horizon," the Premier said in an interview at the Canadian embassy.

The two sides were close to a deal over the summer, in which Canada would have agreed to a cap on the amount of softwood it would export to the United States. That quota, one source said at the time, would have been a little more than 30 per cent of U.S. market share to start, falling to slightly less than 30 per cent over five years, then holding steady for another five.

But talks deadlocked over whether Canada would able to exceed its cap in the event that U.S. industry couldn't produce enough to meet the rest of the demand.

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Canada's Ambassador to the United States, David MacNaughton, said this is still the sticking point in a deal. He pointed out that, as it stands, the United States is importing more lumber from Germany and Russia because it cannot produce enough to fill the market gap left by its punitive duties on Canadian wood.

"We're right down to the last issue that needs to be resolved, which is what we call a 'hot-market provision,'" he said in a panel discussion at a Washington event hosted by online news source Politico. "Rather than taking lumber from Russia, why wouldn't you take it from Canada?"

Mr. MacNaughton accused the U.S. industry of deliberately stonewalling a deal "because they're making a lot of money right now.

"It's unfortunate that we're in a situation where the price of lumber right now is sky-high. It is to the benefit of a few lumber barons. We are ending up in the United States with people not being able to afford to buy new homes or to construct new homes," he said.

The National Association of Home Builders – which has long opposed tariffs – testified at hearings in Washington this week that the proposed trade action would undermine the reconstruction efforts and drive up the cost of housing.

In a hearing this week, Texas home builder Eddie Martin – an executive of the builders' association – said that the U.S. industry cannot even meet current demand for some key softwood products. Based on strong demand, average prices for softwood lumber have risen 22 per cent since the beginning of 2016 and some prices are at historic highs, the association notes.

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"Moving forward, there is going to be a lot of rebuilding," Mr. Martin, the chief executive at Tilson Home Corp., said in his testimony. "Tens of thousands of people, like my employees, are going to be in a bad place financially and increases in material costs will have a real and lasting effect on their ability to have homes."

The chief executive of the U.S. lumber coalition accused Ottawa of using the hurricanes as a "political ploy."

"American towns, cities and, communities should be rebuilt using American products, American workers, and the American spirit of coming out stronger in the face of adversity," coalition CEO Zoltan van Heyningen said in an e-mail. "To the extent that softwood lumber is needed to rebuild, there is ample capacity in the United States to supply American wood to rebuild American homes affected by these storms."