The Canadian government this evening approved a request from Washington to let the United States fire unarmed cruise missiles over a testing range in northern Canada.

The controversial decision, taken at a Cabinet meeting that ran 90 minutes over schedule, was transmitted to Secretary of State George P. Shultz in a letter from Allan MacEachen, Canada's secretary of state for external affairs.

Canadian peace groups, which have protested against the cruise missile tests since Canada signed a five-year weapons-testing agreement with the United States in February, immediately said they would take the decision to court.

MacEachen stressed that Canada's move was closely linked to the North Atlantic Treaty Organization's decision in 1979 to deploy cruise and Pershing II missiles in Europe this year while pursuing a pact with the Soviet Union for limiting intermediate-range missiles in Europe. Canada is a member of NATO.

MacEachen said that the agreement allows Canada to cancel any test flight "in imperative circumstances" and that Canada would reconsider the testing if a U.S.-Soviet agreement on intermediate-range weapons in Europe were reached.

Asked whether this could upset the United States, which wants to test the air-launched missile now being deployed on B-52 bombers no matter what the outcome is of the talks, the minister said, "An arms agreement would be so significant, not only for control itself but for the reduction of political tensions, that one could not ignore it."

In his letter to Shultz, MacEachen wrote, "Now that we have agreed to participate in the development of a major weapons systems, we believe that Canada has an even greater obligation to join in the search for a secure peace. For this reason the Canadian government has resolved to be even more vigorous than in the past in promoting creative disarmament and arms control initiatives."

The Associated Press reported that the U.S. Embassy issued a statement that said in part, "We believe this decision will contribute to the security of both our nation and of our allies by demonstrating our commitment to a strong deterrent and to promote stability."

The five-year agreement, which Washington formally requested last month, will permit the Pentagon to test four to six cruise missiles a year on a flight path 1,400 nautical miles long and 80 nautical miles wide from over the Arctic Ocean, up the Mackenzie River valley, parallel to the Rocky Mountains, across the southern Yukon to a weapons-testing range in northern Alberta.

The main purpose is to evaluate the missile's guidance system-- identical to that of the ground-launched version to be deployed in Europe--over terrain similar to the Soviet Union's. Testing will take place during the first three months of the year when there will be no forest-fire hazard and when the weather will be similar to the most adverse conditions in the Soviet Union.