WASHINGTON — Immigration legislation passed by the Senate would reduce illegal immigration into the U.S. by one-third to one-half beyond what would happen under existing law, the Congressional Budget Office said today.

That’s a significantly greater reduction than the nonpartisan budget office said would have resulted from an earlier version of the bill approved by the Senate Judiciary Committee, which would have cut illegal immigration only by 25 percent.

Partly in response to that earlier finding, senators agreed to greatly boost border security in the bill and take steps against people who overstay their visas. Those changes helped the legislation pass the Democratic-controlled Senate with a bipartisan 68-32 majority last week.

It’s now pending in the Republican-led House, where it faces an uncertain future.

The CBO also said that despite spending $36 billion more on border security than would have happened under earlier versions of the bill, the legislation would still reduce the budget deficit by $158 billion over 10 years and $685 billion in the decade after that. Taxes paid by newly legalized residents, along with other revenue, would outpace new spending for government benefits and other costs under the bill.

The measure, if enacted, would cost the government about $23 billion to implement over the first 10 years.