US Republicans have indicated that plans to criminalise illegal migrants, and those who aid them, may be dropped.
Moves to criminalise illegal migrants have angered protesters
Top party members said they would review the plans, which are part of a bill passed by the House in December.
The provisions have angered pro-immigrant groups who on Monday staged more nationwide protests.
Republicans are split over how to stop more illegal immigrants from entering the US and what to with the estimated 11.5m already in the country.
President George W Bush has proposed the introduction of a guest-worker scheme - but this faces stiff opposition from senior members of his party.
The Senate has so far failed to reach agreement on a compromise deal that would allow illegal immigrants already in the country to apply for US citizenship.
'Feeling the heat'
Any agreement reached in the Senate will have to be reconciled with the tough immigration bill passed by the House of Representatives.
The measures sponsored by Republican Congressman James Sensenbrenner and approved in December include:
- The building of 700 miles (1,130km) of barriers along parts of the border with Mexico
- Making it a felony to remain in the US illegally
- Making it a felony to assist those who are in the country illegally
But in a joint statement on Tuesday, Senate Majority Leader Bill Frist and House Speaker Dennis Hastert raised concerns about the last two provisions.
"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 Republican leaders said.
They also criticised Democrats, saying they had blocked Republican moves to strip the provision to criminalise illegal immigrants from the legislation being debated in the Senate.
Efforts to change the bill to make "unlawful presence" a misdemeanour rather than a felony had been blocked, Republicans said.
Their comments were rejected by the Democratic party, which said the criminalisation of immigrants had been passed by a Republican-led House and then proposed in the Senate by the majority leader.
"[Republicans] are feeling the heat from the hundreds of thousands of people around the country rallying against the bill," said a spokeswoman for House Minority Leader Nancy Pelosi.
The immigration issue is set to become a key one in November's mid-term elections, with Latinos the nation's fastest-growing voting bloc.