The Reagan administration yesterday avoided a potential confrontation with the Democratic leadership of Congress over the timetable for consideration of the recently signed free trade agreement with Canada.

In a formal exchange of letters, the congressional leadership promised to bring the agreement to a vote before adjourning this year, and the administration pledged to cooperate in drafting the legislation to provide the legal underpinnings for the pact to ease trade barriers in an area from the Arctic Circle to the Rio Grande.

The timetable was set in an exchange of letters between Treasury Secretary James A. Baker III and U.S. Trade Representative Clayton K. Yeutter, and House Speaker Jim Wright (D-Tex.), Senate Majority Leader Robert C. Byrd (D-W. Va.), House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) and Senate Finance Committee Chairman Lloyd Bentsen (D-Tex.).

The administration was pressing for early consideration of the free trade agreement, which promises to be one of the major achievements of the Reagan administration in the field of international economics, while the Capitol Hill leadership said Congress was tied up with a major revision of trade law.

Administration officials were concerned that congressional Democrats were planning to hold the free-trade pact hostage to White House acceptance of controversial measures in the trade bill, a tactic the Democrats denied.

But both Democrats and Republicans in Congress were annoyed that they had not been fully consulted before the agreement with Canada was reached and fearful that moving too fast would deprive them of any say in the matter. Under special rules, the agreement will be considered on a congressional "fast track" that allows neither amendments nor delaying tactics.

While there are many objections on Capitol Hill to parts of the agreement, it appears likely that it will win approval. The agreement also needs to be ratified by the Canadian Parliament.

The major sticking point with Congress is a recent Canadian proposal to offer special tariff rebates on fabric to give its clothing industry a competitive edge on exports. The administration said that subsidy violates the spirit and letter of the agreement.

Baker and Yeutter said the legislation will not go to Congress before June 1 unless the leadership and administration agree they can move up the timetable.

"We understand fully the preparatory work necessary to make the fast track work successfully. We want and intend to live up to the spirit as well as the letter of fast track," Baker and Yeutter said in the letter to the congressional leaders.

"We are confident that when it comes to a vote, both houses will conclude that approving the agreement will be one of the most significant achievements of the 100th Congress," Yeutter said.

Bentsen said "all interests come out winners" in the agreement between Congress and the administration. Rostenkowski called the agreement "a reflection of a responsible attitude at both ends of Pennsylvania Avenue."In other trade action yesterday, Rostenkowski and Bentsen released a timetable for conference consideration of the broader trade bill that puts off votes on some of the most contentious items until after the Illinois primary on March 15.