The Senate began floor action yesterday on a bill to overhaul the nation's immigration laws, but only after agreeing to postpone for at least a week consideration of the bill's most controversial provisions.

The Senate is expected to approve the proposal to regain control of the nation's borders by granting amnesty to several million illegal aliens, imposing sanctions on employers who knowingly hire illegal residents, limiting the number of non-refugee immigrants and beefing up the Border Patrol.

Last year, the Senate approved an almost identical immigration package by a vote of 80 to 19, but the measure died in the House.

Yesterday, when Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) first called for initial consideration of the measure, Sens. Alan Cranston (D-Calif.) and Edward M. Kennedy (D-Mass.) objected.

Both sides finally agreed to consider only noncontroversial aspects of the bill yesterday and then resume consideration on the first Monday after the Senate completes action on its budget resolution, which is expected to begin next Monday and last about a week.

This year's House version of the immigration bill was approved by a subcommittee April 6 and is scheduled for consideration by the full Judiciary Committee beginning Tuesday.

It has several differences from the measure on the Senate floor. It proposes a single phase system for permitting illegal aliens already in the country to become permanent resident aliens, instead of a two-tiered system.

It would also require newly legalized aliens to wait four years before they could become eligible for federal welfare benefits, one year longer than otherwise proposed.