WASHINGTON - Senate leaders said today they had won backing from President George W. Bush in their push to pass an immigration law overhaul this election year.

But while the leaders expressed confidence the contested measure could get through the Senate as early as next month, it seemed full action might not come until the end of the year.

After a White House meeting with Bush, criticized earlier for not doing enough to get the legislation approved and for not proposing specific measures in his broad support for a controversial guest-worker program, Senate Judiciary Committee Chairman Arlen Specter said Bush had pledged to do more.

"We had a definitive statement from the president that he wants a comprehensive bill," Specter told reporters. "And he's talking about a way to take the undocumented immigrants who are in the United States today to get in line, not for automatic citizenship, but to get in line."

Senate Majority Leader Bill Frist, a Tennessee Republican, and Senate Democratic Leader Harry Reid of Nevada said they would push to pass a comprehensive bipartisan bill out of the Senate by the end of May.

The Senate bill, which would tighten border security and create the new guest worker program backed by Bush, providing a path to US citizenship for millions of illegal immigrants, got bogged down earlier this month in partisan wrangling.

Bush told reporters there was a good chance Congress would send him comprehensive immigration legislation before the end of the year. While he did not specifically endorse the Senate bill, he said he would work with lawmakers to get a bill through the Senate by the end of May.

That would set the stage for difficult negotiations with the US House of Representatives, which has passed a tough border security and enforcement bill that further criminalizes illegal presence in the United States.

Senators who back the bipartisan Senate bill were clearly pleased following the meeting with Bush.

"After this meeting, I'm convinced that we will pass immigration reform this year," Specter said.

"I think we made great progress today," said Reid.

Bush has long backed immigration reform but offered few specifics other than to say he supported a guest worker program that did not offer automatic citizenship.

Lawmakers sought Bush's help after the Senate bill stalled. Some Republican House members have said they would oppose the Senate version of the legislation.

The Senate bill would give the estimated 11.5 million to 12 million illegal immigrants living in the United States a chance to earn citizenship after they pay a fine, pay back taxes, show an understanding of English and meet other requirements.

Lawmakers, especially Republicans, are divided over Bush's proposal to create a guest worker program and a path to citizenship for illegal immigrants.

Many Republicans oppose any measure that could be seen as forgiving or rewarding people who broke US laws by entering the country without legal papers. They want to concentrate on border security and enforcement of laws banning illegal immigrants from working.

That was the approach taken by the House in a bill that would define illegal immigrants as felons, which has provoked large demonstrations by Hispanics and their supporters across the country.