OTTAWA, JAN. 11 -- Bowing to Canadian demands, the U.S. government agreed today to seek Canadian consent before sending ships through the Northwest Passage, which Canada claims as its territorial waters.

The American accord came in an Arctic Cooperation Agreement, signed here by Secretary of State George P. Shultz and Canadian External Affairs Minister Joe Clark.

But the Reagan Administration, clearly concerned about setting a precedent that could be cited in other international disputes, refused to concede Canada's claims of sovereignty over the straits.

"What we have now significantly advances Canadian interests," Prime Minister Brian Mulroney said.

A statement by President Reagan that was released here said, "This is a pragmatic solution based on our special bilateral relationship . . . It is without prejudice to our respective legal positions and it sets no precedents for other areas."

The decision of the Reagan administration to send the U.S. Coast Guard icebreaker Polar Sea through the Northwest Passage in the summer of 1985, without formally seeking Canada's permission, touched off an angry furor here.

That act was widely depicted here as an example of the way the United States tramples on Canada's rights and, in this case, claims of sovereignty.

The Canadian debate ignored, for the most part, arcane law-of-the-sea issues involved in the complex dispute -- and the fact that the United States not only had consulted Canada before the voyage but had also permitted two Canadian Coast Guard captains to travel on the icebreaker as observers and advisers.

There were angry editorials and political cartoons in Canadian newspapers. The controversy played into the assertions of Canadian nationalists that Mulroney's close relations with Reagan jeopardized Canada's independence.

Ottawa reporters now acknowledge that they may have exaggerated their coverage during that slow summer news period.

Canada claims sovereignty over what it terms the "internal Canadian waters" of the Northwest Passage and has sought to exercise jurisdiction, citing a responsibility to ensure the welfare of the native people who live in the area and to preserve the ecological balance.

The United States recognizes only a 12-mile Canadian coastal jurisdiction in the Arctic and maintains that the Northwest Passage is an international strait.

To yield on this point, the United States has indicated, would weaken the American position against similar claims worldwide -- such as by Libyan leader Moammar Gadhafi in the Gulf of Sidra.

The disagreement here has dragged on for more than two years. During that time, the Mulroney government has acted to assert its sovereignty over the Arctic by basing planes there and deciding to construct a Canadian icebreaker and to buy a fleet of nuclear-powered submarines to patrol the Arctic.

External Affairs Minister Clark has acknowledged that the decision to spend several billion dollars for the submarines was driven more by concern over the United States than because of any fear of Soviet military activity in the Arctic.

Shultz, on a one-day visit, also signed accords facilitating extradition and cooperation against terrorism. He and Clark said they discussed the acid-rain issue, which is a particularly sensitive one here.