By David Ljunggren

OTTAWA (Reuters) - Talks between Canada and the United States to resolve a dispute over exports of softwood lumber are making little progress and the matter likely will return to the courts, sources familiar with the negotiations said on Friday.

U.S. producers complain that Canadian softwood lumber is subsidized, and have in the past launched trade challenges that resulted in the United States imposing billion of dollars in tariffs.

The most recent round of arguments ended with a 2006 deal that expired in October 2015. Both sides agreed to take no action for a year after that, but without a new agreement, U.S. firms look set to file new damage claims.

"The two sides are so far apart right now that a deal looks very unlikely," said one person familiar with the talks.

In March, President Barack Obama and Canadian Prime Minister Justin Trudeau asked officials to work out possible solutions and report back within 100 days.

Although the deadline runs out on June 18, Canadian Trade Minister Chrystia Freeland said the sides would work until June 29, when Obama and Trudeau meet in Ottawa.

"It's a really tough issue and what we're looking for is a good deal. There is a lot of work we have to do," Freeland said.

Representatives from the sides held talks in Canada last month - a meeting that one source described as "not a success" - and in the United States this week.

"While differences remain, U.S. and Canadian negotiators will continue to work to see if a deal can be achieved," said Matt McAlvanah, a U.S. Trade Representative spokesman.

As the U.S. economy recovers, Canadian firms could benefit from more home construction. Exports of softwood lumber totaled C$5.9 billion ($4.6 billion) in 2015, up from C$5.5 billion in 2014, according to Statistics Canada data.

The 2006 agreement said that if prices fell below a certain level, Canadian firms could pay export taxes or agree to quota limits while paying lower tax rates.

One challenge for Canada is that domestic lumber producers are split over the best strategy, say officials in Ottawa.

Firms on the west coast - who have diversified operations by boosting exports to Asia - are more likely to agree to a deal limiting exports, while those in central and eastern Canada want no restrictions.

Major Canadian lumber firms include Canfor Corp <CFP.TO>, West Fraser Timber Co <WFT.TO>, Interfor Corp <IFP.TO> and Resolute Forest Products Inc <RFP.N>.

(With additional reporting by Roberta Rampton in Washington; Editing by Alan Crosby)