WASHINGTON, June 14 — Senate leaders announced an agreement this evening to put a comprehensive immigration bill back on track for further debate and possible passage.

Senators Harry Reid, the Democratic majority leader from Nevada, and Mitch McConnell, the Republican minority leader from Kentucky, agreed on a timetable for the bill and for a limited number of amendments to be offered.

The agreement, coming after President Bush’s pledge earlier today to provide $4.4 billion for border security, revives a bill that had stalled in the Senate and was all but given up for dead.

“We met this evening with several of the senators involved in the immigration bill negotiations,” Mr. Reid and Mr. McConnell said in a statement. “Based on that discussion, the immigration bill will return to the Senate floor after completion of the energy bill.”

The measure would tighten border security, put many of the 12 million or so illegal immigrants in the country on a path to eventual legal status and create a guest-worker program.

The additional money for border security is intended to assuage Republicans who have strongly criticized the plan as amnesty for illegal immigrants.

Mr. Reid and Mr. McConnell said they had agreed that Democrats and Republicans alike would be given a chance to further refine the bill to their liking.

Bringing as many senators as possible on board is crucial in the Senate, since 60 votes are required there to overcome procedural hurdles in order to vote on the bill itself. With lawmakers, and their constituents, wanting different things in an immigration bill, support can easily erode.

Moreover, any bill that emerges from the Senate will have to be reconciled with what the House of Representatives passes, assuming that the House passes a bill. But this evening’s accord, however tentative, rekindled hopes that a bill might be approved by the full Congress this year.

The announcement followed renewed lobbying by President Bush, who is eager to have a bill overhauling the immigration system and who has been emphasizing border security in recent days. He has been doing so to appease those lawmakers who complain that the bill as it stands would grant amnesty to lawmakers, no matter what its supporters say to the contrary.

Mr. Bush’s emphasis on security, backed up by his push for more than $4 billion aimed at “securing our borders and enforcing our laws at the work site,” plus continuing sentiment among lawmakers to give the bill another chance, lay behind the accord between Mr. Reid and Mr. McConnell.

Only a week ago, Mr. Reid declared with some disgust, “We are finished with this for the time being.” Now, things are apparently back on track, at least for the time being.