Canadian Prime Minister Joe Clark formally resigned yesterday and called for new national elections on Feb. 18, during what is normally the coldest period of the year in one of the coldest countries in the world.

In what sounded like a campaign kickoff, Clark said his Progressive Conservative government was defeated because it is "prepared to face honestly the hard realities confronting Canada."

He said that, if reelected, he would reintroduce the same austerity budget that precipitated the defeat of his minority government in the House of Commons Thursday night.

Speaking at a news conference in Ottawa, Clark conceded that the unexpected government crisis would hurt the cause of federalist supporters in Quebec, where the separatist government plans to hold a referendum next spring on its proposal to make the French-speaking province independent.

Clark, who will remain as caretaker prime minister until Feb. 18, termed "unfortunate" the adverse effect the crisis is expected to have on the Quebec referendum. But he charged that "irresponsible actions" by the opposition Liberal and New Democratic parties precipitated the crisis.

The Liberals, the main opposition group that forced the new elections, were engaged in intense maneuvering yesterday to select their standardbearer. Pierre Trudeau, who was forced out of the prime minister's office when the Liberals lost the national elections last May, resigned as party leader only three weeks ago.

Late last night, after 10 hours of intense maneuvering, the Liberal caucus overwhelminglly agreed to urge Trudeau to lead the party in the election. Trudeau met with the caucus earlier in the day, and would not comment on whether he would be a candidate.

A draft-Trudeau movement among some party stalwarts and an alternative plan to appoint former finance minister Donald Macdonald as interim party leader have produced a split in the Liberal leadership.

The most recent Gallup poll revealed a sharp decline in the Conservative government's popularity, indicating a Liberal victory in any early elections. But diplomats in Ottawa say that the Liberals' leadership problems and public distaste for political campaigns during the coldest winter months make the toppling of Clark a high-risk game for the Liberals.

There were renewed efforts yesterday to draft the popular former Cabinet minister John Turner to take the Liberal leadership. He rejected similar efforts two weeks ago. A meeting of the party's national executive body was scheduled today in Ottawa.

A majority of the executive's 32 members are reported to oppose the draft-Trudeau movement because of his unpopularity in English Canada.

Meanwhile, Quebec Premier Rene Levesque attacked as "cruel and insulting" a Canadian Supreme Court ruling that declared invalid parts of Quebec's language law making French the sole official language in the province. However, the Quebec legislature quickly complied with the court ruling by passing special legislation yesterday that legalized English translations of all laws it passed in French only during the past two years.