WASHINGTON – The Senate yesterday agreed to exclude as many as 500,000 criminal aliens from a plan that would offer undocumented immigrants legal status, while approving the construction of 350 miles of fencing along the America-Mexico border.

The Senate also rejected an amendment that would have completely eliminated the plan to offer a path to citizenship to undocumented immigrants, as lawmakers debate the largest overhaul of American immigration policies since 1986.

“Not only are we actually getting to debate and vote on amendments, but we’re actually seeing bipartisan support,” Senator Cornyn, a Republican of Texas, said. “I hope that this establishes some rhythm and momentum for the bill that will allow us to be successful.”

The Senate is working through more than 20 amendments in an effort to complete work before the end of the month on immigration legislation that would strengthen border security, create a new guest worker program, and allow an estimated 11 million undocumented immigrants to apply for legal status.

Senators yesterday rejected two proposals that would have removed key provisions of the legislation. By a vote of 66-33, lawmakers turned aside an amendment sponsored by Senator Vitter, a Republican of Louisiana, to block all immigrants in America illegally from gaining legal status. On Tuesday, senators voted 69-28 to set aside an amendment that would have eliminated the guest worker program.

Senate consideration of the legislation stalled in April because of disagreements between Republicans and Democrats on how to consider amendments, including the one approved yesterday that bars criminal aliens from the legalization process.

The amendment would bar immigrant felons, those who have committed three or more misdemeanors, or those who have committed crimes that make them ineligible for visas from participating in the legalization program.

In a compromise on the proposal, on Tuesday night senators agreed to let some immigrants who have ignored deportation orders to remain eligible for legal status if they show family hardship or prove they did not receive adequate notice of a deportation hearing.

“We don’t want people who are convicted felons, guilty of crimes, to be eligible for citizenship in this country,” Senator McCain, a Republican of Arizona, said. “At the same time, we didn’t want to go too far.”

The provisions will “treat individuals fairly, welcome those who should be welcomed, and exclude those who should be excluded,” Senator Kennedy, a Democrat of Massachusetts, said.

The fencing was approved 83-16 in a vote on an amendment by Senator Sessions, a Republican of Alabama. It calls for 350 miles of border fencing and 500 miles of vehicle barriers.

“It sends a signal that open border days are over,” he said before the vote. “Good fences make good neighbors.”

Mr. Kennedy objected to the proposal because it could lead to even more fences. “That’s the down payment for fencing the whole border,” he said.

Senators also have approved amendments lowering the number of guest worker visas to 200,000 a year, setting wage rules for the program, and preventing it from being used where more than 9% of low-skilled American workers are unemployed.

Other amendments the Senate is likely to consider would require employers to advertise jobs to Americans before foreign employees can gain permanent residency and would make English the nation’s official language.

Majority Leader Frist, a Republican of Tennessee, has said the Senate will complete work on the measure by the end of the month.

Congress last passed such broad immigration legislation in 1986, when it approved a program that granted legal status to as many as 3 million undocumented immigrants and criminalized the hiring of those in America illegally.

Legislation passed by the Senate will have to be reconciled with a House measure passed last year that backs 700 miles of fencing and does not address a work program or legalization of undocumented immigrants.

“Everybody realizes that where this bill will be written is in the conference committee between the House and the Senate,” Mr. Cornyn told reporters yesterday. “The question is going to be how we reconcile our differences with the House.”