Debate likely to resume next week

Frist said senators should commit "full session days" to the bill, "with a considerable number of amendments debated and voted on each day," though he would not specify whether the process would take one or two weeks.

The announcement came after Frist reached an agreement with Senate Democratic leader Harry Reid on the makeup of the House-Senate committee that will be charged with reconciling the two chambers' different versions of the bill and coming up with a unified piece of legislation.

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Reid, for his part, said he welcomed the bill's return to the Senate floor.

"America's immigration system is broken, and our national security depends on Republicans and Democrats finding common ground to fix it. The assurances I have received from Senator Frist make me hopeful we can finally move forward on real comprehensive reform," Reid said.

The immigration issue has divided the Republican Party, with some members of Congress pushing for strict penalties against illegal immigrants and those who employ or assist them.

Proposed legislation passed in the House of Representatives in December would criminalise illegal residency and construct a fence along a vast section of the southern US border.