A written statement by House Speaker Dennis Hastert of Illinois and Senate Majority Leader Bill Frist of Tennessee, did not say whether they would seek legislation subjecting illegal immigrants to misdemeanor prosecution or possibly a civil penalty such as a fine.
"It remains our intent to produce a strong border security bill that will not make unlawful presence in the United States a felony," the two men said. An estimated 11 million men, women and children are in the United States illegally.
The Republican-controlled House passed legislation late last year that is generally limited to border security measures. It makes illegal immigrants subject to felony prosecution.
Senate efforts to write a broader bill — covering border security, a guest worker program and a path to citizenship for many of the 11 million in the country illegally — are gridlocked with lawmakers on a two-week vacation.
Frist has said he intends to bring the issue back to the Senate floor, although he stopped short of a flat commitment and the prospects for passage of an election-year immigration bill are uncertain.
The late-afternoon statement by the top GOP leaders in both houses came after days of large street demonstrations by protesters opposed to criminal penalties for illegal immigrants.
A CBS News poll (.pdf) released this week finds most Americans – 74 percent –think illegal immigrants should be able to stay and work in the U.S. if they certain criteria, including that they've been in the country at least five years and that they pay a fine and any back taxes owed. Those criteria roughly match those in the Senate compromise bill that was shelved last week.
Sen. Edward M. Kennedy, D- Mass., dismissed the proposal by the GOP leadership, saying: "Actions speak louder than words, and there's no running away from the fact that the Republican House passed a bill, and Senator Frist offered one, that criminalizes immigrants."
"This debate shouldn't be about making criminals out of hardworking families ... but rather about strengthening our national security and enacting a law that reflects our best values and our humanity," Kennedy said.
The question of a penalty has dogged the debate for months and been the subject of intense political maneuvering.
GOP aides pointed out that Rep. James Sensenbrenner, R-Wis., chairman of the House Judiciary Committee, had tried during debate on the House floor to reduce the penalty to a misdemeanor.
The attempt failed on a vote of 257-164, with 65 Republicans and 191 Democrats opposed. Many of the Democrats, including members of the Hispanic Congressional Caucus, indicated at the time they favored no criminal penalties, and opposed the suggested change.
In their statement, Hastert and Frist said the Democrats who did so had demonstrated a "lack of compassion." In addition, they renewed the charge that Senate Democratic leader Harry Reid is seeking to "block action on immigration legislation."
Reid has denied the charges.
While they leveled their accusations at Reid, the GOP leadership has been struggling with internal divisions.
Several House Republican conservatives have vociferously denounce Senate proposals as amnesty for lawbreakers.
And while Frist praised the leading Senate proposal last week as a "huge breakthrough," he was the only member of the GOP leadership to embrace it. Two other members of the group, Sens. Jon Kyl of Arizona and Kay Bailey Hutchison of Texas, voiced their opposition. Sen. Rick Santorum of Pennsylvania opposes the measure, according to a spokesman.
Sen. Elizabeth Dole of North Carolina, who heads the party's senatorial campaign committee, declined this week through an aide to take a position on the bill.
A spokesman for Sen. Mitch McConnell, the second-ranking Republican, sidestepped a question by saying the Kentucky lawmaker favors a comprehensive approach.