By Jeff Mason

WASHINGTON (Reuters) – President Barack Obama said on Tuesday he could support the House of Representatives taking a piece-by-piece approach to changing immigration policy as long as key elements such as a “pathway to citizenship” for undocumented immigrants were included.

The White House had hoped a broad bill to reform immigration rules would be the president’s signature achievement this year, but the effort has stalled in the House after passing with bipartisan support in the Senate.

In an interview with Noticias Telemundo, Obama said he could back efforts in the House to advance elements of immigration reform one at a time – rather than all at once as the Senate did – as long as all of his priorities were part of the outcome.

“I’m happy to let the House work its will as long as the bill that ends up on my desk speaks to the central issues that have to be resolved,” he said, citing his priorities of stronger border security, penalties for employers who take advantage of undocumented workers, and a pathway to citizenship for immigrants who are in the country illegally.

“If those elements are contained in a bill, whether they come through the House a little bit at a time or they come in one fell swoop … I’m less concerned about process, I’m more interested in making sure it gets done,” he said.

Advocates are reluctant to support a piece-by-piece approach out of concern that the elements most popular among Republicans, such as tougher border security, would be passed while the pathway to citizenship for some 11 million undocumented immigrants would not.

A spokesman for Speaker of the House John Boehner, a Republican, welcomed Obama’s comments.

“If immigration reform is going to work, it is essential that we have the confidence of the American people that it’s done the right way,” said Brendan Buck. “That means a deliberate, step-by-step approach, not another massive Obamacare-style bill that people don’t understand.”

Obama urged Boehner to bring the issue to a vote. The White House believes enough Democrats would support reform efforts to make up for the Republicans, who have a majority in the chamber, who would oppose it.

Boehner does not want to bring the issue to the floor of the House without the support of a majority of his fellow Republicans.

“We’ve got a majority of members of Congress, Democrats and some Republicans, in the House of Representatives, who would vote for it right now if it hits,” Obama said.

Obama said it was “not an option” for his administration to freeze deportations of undocumented immigrants while waiting for immigration reform to pass. The president has come under sharp criticism from activists for presiding over high numbers of deportations despite his support for reform.

If the House were to pass one bill or several bills reforming U.S. immigration laws, that could trigger a formal negotiation between the House and the Senate, which in June passed a comprehensive measure including a pathway to citizenship for undocumented U.S. residents.

In that case, a group of House and Senate negotiators would attempt to come up with one bill that could pass both chambers and be signed into law by Obama. But many conservative House Republicans, who oppose a comprehensive immigration bill, are reluctant to get into such a negotiation with the Senate, fearing they could be cornered into backing the pathway to citizenship.

(Additional reporting by Richard Cowan,; editing by Jackie Frank)