Washington (CNN) - President Barack Obama renewed his push on Tuesday for House Republicans to approve most of what exists in the Senate-passed version of comprehensive immigration reform. But he signaled a willingness to compromise.
At an event with law enforcement officials, Obama said he was "not hell-bent" on seeing every word from the Senate version in any immigration bill that might reach his desk.
"But there are core principles that we have to get done," Obama added, noting his support for much of what the Senate approved last year, 68-32.
The bill "would give law enforcement a better idea of who's in the country," he said. "Public opinion is on our side."
Accusing a handful of House Republicans of "blocking" passage of a final reform bill, Obama said he wants to negotiate.
"If they've got ideas, I'm happy to talk," he said.
A White House official noted the Senate measure has the support of both Republicans and Democrats, as well as well-respected figures from business, religious and law enforcement communities.
Tuesday's meeting marked the first time Obama has sat down with law enforcement to make the case for immigration reform, the official said.
Obama aides believe House Speaker John Boehner has not closed the door on the Senate measure. So Obama is "still pushing," the official said.
The Senate approved the immigration reform bill last June, that was pushed by a bipartisan “Gang of Eight.”
The measure, which stalled in the House, includes an eventual pathway to citizenship for most undocumented immigrants, which is strongly opposed by many conservatives.
On Monday, Boehner acknowledged that he still faces resistance from a group of Republicans.
"I need to work with my colleagues and bring them along. And while I feel strongly about the need to deal with immigration reform, I have got to bring these members along," Boehner said at an event hosted by the San Antonio Chamber of Commerce.
But a senior House Republican told CNN on Tuesday that "Speaker Boehner has been clearer than crystal many, many times that we are not taking up the 'Gang' bill, and we're not going to Conference on the Senate 'Gang' bill. It's deader than disco."
U.S. Chamber of Commerce President Tom Donohue said Monday that the GOP shouldn't field a presidential candidate in the next race if Congress fails to pass immigration reform this year.
"If the Republicans don't do it, they shouldn't bother to run a candidate in 2016," Donohue said, in an attention grabbing moment.
The chamber, which represents business interests, has made immigration reform a focus.
Donohue added that "we're absolutely crazy if we don't take advantage of having passed an immigration bill out of the Senate because going back and doing it again might be harder."
CNN's Deirdre Walsh and Paul Steinhauser contributed to this report