Prime Minister Pierre Trudeau today announced his government's support for a pipeline across Canada to carry Alaskan gas to the United States.

But the pipeline will be built only if the U.S. government agrees to Canadian conditions on its timing, routing and financing and to compensation for social and environmental costs, said Trudeau.

Canadian officials, said one of the conditions will be asurcharge, to be paid by American consumers of natural gas, fo the creation of a $200 million fund to offset the pipeline's social and environmental cost to Canada.

President Carter, who has until Sept. 1 to present a decision on the pipeline to Congress, said in Plains today that "If we can reach some degree of agreement with the Canadians by the, I think we'll be able to stay on schedule."

Expressing optimism, Carter added: "If all goes according to schedule we'll start negotiating with them within about a week."

Trudeau, who made his announcement at a press conference, said: "We're obviously not going to build it if it's not a significant benefit to Canada. We'd like to have the Americans pay as much as possible (of the cost of pipeline). But we have to be reasonable."

Trudeau's announcement set the stage for negotiations between the United States and Canada over the pipeline. "There are going to be tough negotiations," said Trudeau. "But we are confident [they] will succeed."

Trudeau said he had spoken to President Carter earlier today by telephone and received assurances that the U.S. government prefers a trans-Canada pipeline to a rival trans-Alaska project. But, said Trudeau, if Canada asks for too much that preference could change.

The proposed trans-Canada pipeline would follow the route of the existing Alaska oil pipeline as far as Fairbanks and then turn east through the Yukon in northern Canada and then south to the Midwestern United States. It would cost an estimated $8.6 billion and 2,750 miles of pipe would be laid, more than 2,000 miles in Canada.

The project, known as the Alean pipeline, is sponsored by Northwest Pipeline Corp. of Salt Lake City and Foothills pipe Lines Ltd. of Calgary.

The two companies bear out another joint American-Canadian consortium planning a route down the Mackenize Valley in Northern Canada, which was ruled out by the Canadian government for environmental and social reasons. Some members of the unsuccessful consortium have since joined the Alcan group.

Still in the running is El Paso Natural Gas Co. of Houston, which is proposing a pipeline across Alaska to Valdez, where the gas would be liquefied and sent to the lower 48 states by tanker.

The Alcan project is cheaper than the El Paso pipeline, but tough conditions imposed by the Candian government could narrow the difference Trudeau refused to specify the conditions the Canadian government will be asking that the pipeline to rerouted through Dawson City, site of the famous Klodike gold rush, to bring it closer to the source of Candian gas. Canada hopes to hook up its own northern gas reserves with the American pipeline at Dawson City for delivery to markets in the south of Canada.

The Canadian government will also seek U.S. approval of an "all-events tariff" for gas carried by the pipeline. Such a tariff would mean that American consumers would have to pay for the pipeline even if no gas is ever delivered through it.

American negotiators, led by Les Goldman, a senior adviser to Secretary of Energy James Schlesinger, have already told Canada in preliminary meeting that these conditions are unacceptable.

However, the Canadian government took this as a bargaining position of the United States and not the final word on the matter.

Trudeau expressed the hope that the negotiations would be "very open" and that neither side would try to bluff the other with talk of alternative routes.

But he said that if the United States rejects Canada's conditions, "We still have a lot of other options." Canada could build its own pipeline to northern Canadian gas reserves instead of hooking up with a U.S. pipeline, he said.