Canadian Prime Minister Pierre Trudeau yesterday gave public support to the interim nuclear arms reduction proposals President Reagan has made to the Soviets, signaling for the first time that he is likely to approve U.S. requests to test cruise missiles in Canada.

After a White House meeting with Reagan, Trudeau, in his official departure statement, said he felt that the president's recent arms control initiatives have demonstrated to the western alliance and anti-nuclear groups that the United States is "not determined to escalate any arms race," and wants a lasting peace.

About 80,000 Canadians demonstrated in "Refuse the Cruise" rallies last weekend after Trudeau signed a memorandum of understanding with the United States for testing cruise missiles over terrain in western Canada that is similar to areas around Moscow.

However, Trudeau said final Canadian approval of the tests would be linked to signs of U.S. flexiblity in arms talks. Vice President Bush and Secretary of State George P. Shultz have met with Canadian officials recently on the cruise test issue without getting any strong signal of support.

"I've been encouraged by the steps you have taken, Mr. President, in the past months when you proposed an interim solution different from the zero option," Trudeau said in his departure statement. "I think these are all initiatives we need in NATO so that our people will understand that we want peace."

After the meeting, a senior official told reporters that the administration is "generally, positively optimistic that when our request is submitted it will be considered favorably."

In addition to discussing the U.S. stance on arms talks, administration officials reported that the prime minister and president reviewed prospects for the May 28-30 economic conference of western allies in Williamsburg.

Trudeau's visit was the latest in a series of meetings the president is having with leaders of key western nations who will attend the economic conference. West German Chancellor Helmut Kohl and Gaston Thorn of the European Economic Community have been to the White House in the last two weeks, and the leaders of Great Britain, France, Italy and Japan are scheduled to visit the president within the next month.

The object of the pre-conference meetings is to prevent a repeat of last year's summit at Versailles, when disagreements about western trade policy toward the Soviet Union bogged down the talks.

The president won Trudeau's support for his wish to hold the Williamsburg talks without a prearranged agenda or attempting to reach formal agreements at the meeting and that it be an effort to make sure the "recovery is deep and long lasting."

"I was particularly happy that you confirmed to me," Trudeau said in his statement, "that you would be determined . . . to ensure that the talks at Williamsburg were unstructured and hopefully that we won't be meeting in order to justify an agenda."