Shares of major Canadian lumber producers came under pressure Monday after an analyst doused cold water on hope for a solution to the cross-border softwood dispute any time soon.

BMO Capital Markets downgraded West Fraser Timber (WFT.TO), Canfor (CFP.TO) and Interfor (IFP.TO) to Market Perform amid the apparent lack of hope for an immediate resolution.

"We believe prospects for a near-term settlement of the U.S./Canadian lumber dispute have faded," wrote Analyst Mark Wilde in a report to clients.

"Comments by high-ranking Canadian and government officials and some U.S. corporate executives have fed hopes that a negotiated settlement is close at hand. Our sources report little substantive negotiation..."

The United States has imposed two rounds of levies on Canadian softwood in recent months. On April 24, it announced countervailing duties reaching as high as 24.12 per cent. On June 26, the U.S. Commerce Department followed up with antidumping duties ranging from 4.59 to 7.72 per cent.

In between those two announcements, the government of Canada stepped in with an $867-million support package for the forestry industry. 

Foreign Affairs Minister Chrystia Freeland said on Monday softwood remains a priority issue for the government, but gave no indication a settlement is imminent.

"We want a good deal and we think that is achievable; but we don't want just any deal -- and the Americans know that," she told lawmakers during a presentation to the House Standing Committee on International Trade.

"At the moment, the softwood lumber negotiations will continue in parallel with NAFTA negotiations."

Facing uncertainty about the outlook for a softwood solution, combined with the Canadian dollar's recent run higher, BMO reckons West Fraser, Canfor and Interfor could all see their earnings come under pressure in the 2018 fiscal year and thus there's limited upside potential for their shares.