ALBANY – Senior Cuomo administration officials met Thursday with Canadian members of the Peace Bridge Authority to try, again, to resolve the bitter dispute over future construction plans designed to ease congestion on the busy span between Buffalo and Fort Erie, Ont.

The meeting, at an undisclosed location in Canada, included Lt. Gov. Robert Duffy but produced no resolution. It was the second meeting in recent weeks between Duffy and Anthony Annunziata, a Canadian who is chairman of the Peace Bridge Authority. Also attending was Howard Glaser, the governor’s director of state operations, whose critical letter in April to the Canadian transport minister added fuel to the feud, Canadians say.

A request for an interview with Duffy about the session was rejected. The Cuomo administration declined to comment on the meeting but called it productive.

Annunziata, who has not been shy about representing Canadian interests in the fight against New York, declined to provide any details about the meeting.

But his characterization of the status of the dispute did not offer encouraging signs after the meeting. “I’m just hoping cooler heads prevail. I don’t want to say anything more right now,” he said.

He predicted court challenges if Albany approves legislation to dissolve the binational bridge authority in as soon as one year. Such a prospect could delay a range of bridge improvements.

The disagreement, which has attracted the attention of top federal officials in both countries, has involved a nasty war of words between the Cuomo administration and Canadian bridge authority members. Gov. Andrew M. Cuomo has said he is simply trying to jump-start long-stalled plans for work on the Buffalo side of the bridge to alleviate congestion and speed along commerce, while Canadians have accused Albany officials of not sharing details about the work envisioned for the U.S. side.

The most immediate concerns for Canadians is legislation speeding through the State Legislature that its sponsors hope will lead to the dissolution of the bridge authority, which dates back to 1933. Sen. Mark Grisanti, R-Buffalo, and Assemblyman Sean Ryan, D-Buffalo, say the board has outlived its usefulness. Their legislation moved through several committees, including the Assembly Ways and Means Committee, on Wednesday; it passed by a 21-11 vote in the Democratic-led committee with the sole Democratic no vote coming from Assemblyman Robin Schimminger of Kenmore.

“What happens to staff, revenues, tolls?” Annunziata asked. He said Canadians spend nearly $1 billion in Erie and Niagara counties annually. “If there is unpredictability on the bridge with respect to wait times, people will avoid the bridge. And a 10 percent avoidance would result in a $100 million economic impact to Western New York,” he said.