Fears of a constitutional crisis in Canada arose today when Prime Minister Pierre Trudeau and the premier of the province of Alberta ended two days of negotiations with failure to reach agreement on a new price for oil.

Peter Lougheed, the premier of Alberta, told a news conference he was returning to his Western province to consult with his Progressive Conservative government and plan their next move. One probable move would be a unilateral decision by Alberta, which produces most of Canada's oil, todefy the federal government and raise the price of its oil on its own, perhaps by Aug. 1.

Should that occur, Trudeau and his Liberal party government would surely attempt top stop Alberta, either through the courts or through the Parliament, which is now in summer recess. Although the provinces, under the constitution, control all natural resources, including oil, the federal government has the power to regulate natinal trade.

"We may have to recall Parliament," Trudeau told a news conference. "I don't know. It depends, once again, on what Alberta does."

Both Trudeau and Lougheed, in separate news conferences, seemed intent on avoiding rhetoric that would aggravate their differences, and both tried to play down the mood of crisis and confrontation.

Trudeau, however, appeared to try more than Lougheed.

"I do not see the ceiling falling on our heads," "We have failed in negotiations many times before without the country going into ruin."

For the part, Lougheed, when asked if the impending crisis would destroy the country, replied, "That's an overstatement."

But the premier of Alberta did say that he and Trudeau had met because "we were trying to avoid the obvious confrontation that's coming to Canada."

Although the two days of talks focused on the issue of oil prices, they reflected the problems of Western alienatin and provinviol powers, which in recent weeks have replaced Quebec separatism as a symbol of disunity within Canada.

According to separate statements issued by Trudeau and Lougheed today, they were far apart on three issues.

Lougheed wanted the price of Canadian oil, now $14.75 a barrel in Canadian currency (the Canadian dollar is equal to about 87 U.S. cents), to increase by $2 in the rest of this year $5 in 1981 and 1982, an estimated $5.50 in 1983, and an estimated $5 at the beginning of 1984. More important, Lougheed insisted that the Canadian price approach the world price. Trudeau offered less and rejected any tie to the world price.

The two leaders also differed on waysof increasing the federal share of revenues, at present only 10 percent.

Lougheed also rejected as unconstitutional a Trudeau proposal that the federal government levy an export tax on natural gas sold outside Canada.