Prime Minister Pierre Trudeau called yesterday for a renewed sense of common purpose to combat widespread "uncertainty" about Canada's future, and said that "this process of renewal must be based firmly on new partnerships" between Ottawa and the provinces.

Speaking to the premiers of Canada's 10 provinces, Trudeau acknowledged "our current problems" that include a 9 percent unemployment rate and 9.5 percent inflation. His government, he said, is proposing a set of goals that would reduce both figures to roughly 5 percent by 1981.

But Trudeau did not spell out in detail his "new partnership" proposals and he appeared to be reacting in response to a threat by the separatist government of Quebec to seek independence next year.

Trudeau's appeal for support came at the opening session of the three-day annual conference of provincial leaders. The sessions are being carried live on national television.

Because of strong regionalism and Canada's parliamentary system, which has only one federal house, the provincial leaders' conference has emerged over the past two decades as an extra-constitutional institution that plays a role similar in many ways to the U.S. Senate.

In periods of difficulties, the Ottawa government has repeatedly turned to this institution, composed of strong regional figures, to win backing on important issues. Such measures as a national health insurance plan, a national pension program and uniform energy prices were resolved at previous conferences.

Trudeau turned again to the conference yesterday, partly because his government's inability to cope with the present economic difficulties and partly because 60 percent of all government spending in Canada is in the hands of provincial premiers.

Rene Levesque, the premier of Quebec who is seeking independence for his French-speaking province and is pledged to conduct a plebiscite on the issue next year, promptly suggested that Trudeau was using the forum to share the blame for economic setbacks.

Levesque blamed the federal government for the "deplorable" state of the Canadian economy and said that the meeting was a pre-election maneuver. It is widely believed that Trudeau will call for general elections sometime this year.

But Levesque said he would try to "do my best" during the meeting, which is devoted to discussions of medium-term economic strategy, adding that perhaps "once again we are involving ourselves in an exercise of futility."

Some concrete agreements between the federal government and the provinces are expected to be reached, however. Behind the highly technical discussions here there is a fundamental debate on the future of Canadian federation.

"Although we represent 10 provinces, six or seven regions and the entire political spectrum," Trudeau said, "we can find common cause and work to common purposes. For the aspirations of Canadians will be realized only if we can create a renewed sense of common purpose. This process of renewal must be based firmly on new partnerships between governments and Canadians and their government."

Apart from establishing economic goals, the Trudeau government is proposing incentives for private industry and changes in the relationship between the central government and the provinces that would provide for a greater degree of flexibility by federal authorities.