President Obama sought Friday to accelerate momentum toward an overhaul of immigration laws, signaling that he is open to a middle-ground agreement with Republicans that a growing number of lawmakers and advocates think could achieve a far-reaching deal this year.

Obama suggested in a pair of interviews that the ideological gap is narrowing between the parties, a day after House GOP leaders said they would pursue changes that would allow illegal immigrants to remain in the country legally. The president indicated that there is flexibility in a longtime White House demand that any deal must include a special path to citizenship for the nation’s 11 million undocumented immigrants.

The plan House Speaker John A. Boehner (R-Ohio) outlined Thursday is “moving in the direction of the principles that I have laid out,” Obama said Friday in an online video chat. “There are still some differences. Obviously, the devil is in the details, but it is my firm belief that we can get immigration reform done this year.”

In another interview with CNN that aired Friday, Obama said that if Boehner were to pursue a plan that ended the deportation of most illegal immigrants and allowed them to pursue citizenship under existing channels, “I’m not sure how wide the divide ends up being” with Democratic proposals.

Obama’s remarks represented a shift from the administration’s hard-line stance that most illegal immigrants must receive a more direct and faster route to citizenship, reflected in the 13-year path included in a bipartisan Senate bill approved last summer. Latino and Asian American advocates for immigration reform, who overwhelmingly supported Obama’s reelection bid in 2012, have long pressed the White House to stand firm on that point.

Administration officials, key congressional allies and some reform advocates said Friday that the president’s rhetoric reflects an emerging understanding among Democrats that they must meet the House GOP’s shifting stance with some compromise of their own if they hope to strike a deal to end continued mass deportations.

“What he is saying is, ‘I am respectful of the Republican majority,’ ” said Rep. Luis V. Gutierrez (D-Ill.), a leading advocate on immigration who has criticized the Obama administration’s deportation policies.

“If your standard is citizenship for everyone immediately or no immigration reform at all, you are going to get no immigration reform at all,” Gutierrez said. “I think this is a step in right direction. I have said millions should have a pathway to citizenship, legalize all and end these deportations.”

Various immigration advocacy groups also said they welcomed Boehner’s principles as a way to renew negotiations. Frank Sharry, executive director of America’s Voice, a leading advocacy group, said Obama’s accommodating tone was intended to show “respect to speaker to Speaker Boehner and give room to Republicans. I think that’s a smart strategy.”

Both sides cautioned that a long, uncertain road remains during a midterm election year. Immigration reform holds risks for both parties, particularly Republicans who fear that a vote on the controversial issue could jeopardize their standing among conservative voters.

Rep. Mario Diaz-Balart (R-Fla.), who has championed reform in the House, said the GOP caucus was divided into three camps when Boehner announced his principles at a retreat this week: Some members are outright opposed, another group wants to pursue some kind of legislative fix, and a third group worries about the politics during an election year.

Diaz-Balart said a key concern among those pushing to pursue legislation is that they do not trust Obama, or future presidents, to strictly enforce border security laws if current illegal immigrants are given legal status. Obama said two years ago that his administration would defer deportations of young immigrants brought to the country illegally by their parents.

Boehner’s principles aim to make it more difficult for the executive branch to use discretion when implementing immigration laws.

“There is, and this is not a surprise, a great deal of distrust on behalf of Republicans in the House to this administration,” Diaz-Balart said. “Here is the question: Can we put together legislation that secures the borders and interior security, and make sure this and future administrations have to enforce the border security whether they like it or not? Do we have that leverage? I think the answer is yes.”

Even so, some conservatives and liberal groups denounced the emerging framework.

Sen. Jeff Sessions (R-Ala.), a leading critic of legalization and citizenship for illegal immigrants who has been organizing opposition in the House, said that “while Democrat leaders and interest groups appear satisfied, this document was not voted upon by the GOP conference and clearly does not represent the consensus of Republican members.”

The AFL-CIO, which backed Obama’s immigration push last year, demanded that any deal include a special path to citizenship, as envisioned by the Senate. Union President Richard Trumka called the House plan a “flimsy document that only serves to underscore the callous attitude Republicans have toward our nation’s immigrants.”