Canada is sure to ease its limit on exporting natural gas to the United States once the pipeline is built across Canada from Alaska to the Lower 43, Energy Secretary James R. Schlesinger Jr. said yesterday.

Schlesinger told the Senate Energy Committee the United States has "no hard, firm contract" about getting more Canadian gas.

"But it is clear we will get more (Canadian) gas than we otherwise would have gotten had the Alcan pipeline not been built.

President Carter has chosen the route proposed by Alcan Pipeline Co., a decision subject to congressional review. The route would fellow that of the trans-Alaska oil pipeline, then head southeastward, splitting in Canada into two lines that would continue to the West Coast and the Midwest.

The Alcan pipeline system will deliver more natural gas at less cost to a greater number of Americans than any other transportation system," Schlesinger said.

Sen. Ted Stevens (R-Alaska) mentioned Canada's limiting the amount of natural gas it sells to the United States.

Schlesinger said that compared with EI Paso Co.'s Alaska plan for an "all-America" route, the Alcan route has "significantly lower cost of service than EI Paso . . . an ultimate savings of $6 billion for U.S. consumers over the life of the Alcan project."

Because of Alcan line can carry some Canadian natural gas, Stevens asked if "the limit on export of gas to the United States will be expanded and we can expect increased Canadian exports."

Schlesinger replied, "There is no question that we will get more gas if we need that gas, senator."

Stevens than asked if it is possible provincial governments will ignore the Canadian-U.S. agreements on the line.

"It is the provincial governments that have the authority," Stevens said.

Schlesinger said, "We are doubly protected" because the Canadian government will guarantee its agreements - that is, guarantee compliance of all involved.