WASHINGTON — Advocates are demanding that President Barack Obama use his powers as chief executive to stop deportations of more people among the estimated 11 million immigrants living here illegally. The president is obliging, but in a bit-by-bit way that doesn’t satisfy groups frustrated by Republicans’ slow-walking of immigration legislation in the House.

Obama last year acted on his own to halt deportations for some young immigrants living in the country illegally who arrived as children. So far more than 550,000 young immigrants have been allowed to stay under the program, which also lets the immigrants get work permits good for two years.

Republicans pushed a bill through the House earlier this year to resume those deportations, but the Senate never acted on it and Obama’s directive is still in place. Still, the vote was a clear sign of Republican opposition to what some lawmakers have called “backdoor amnesty” through Obama’s unilateral executive actions.

Similar limited actions by the White House have just whetted the appetite of immigration advocates for more of them, now that wide-ranging immigration legislation that would offer eventual citizenship to some immigrants living here illegally is stalled in the House.

“Executive order” was the rallying cry of hecklers at an Obama Democratic fundraiser Monday in San Francisco.

“Stop deportations! Stop deportations!” audience members shouted at a separate event after Obama was interrupted midspeech by a young man who said his family has been separated for 19 months. Both events underscored dissatisfaction with the Democratic president, not only over the stalled immigration overhaul but the administration’s policies.

Obama responded with a brief lesson on the constitutional limits on his power.

“If, in fact, I could solve all these problems without passing laws in Congress, then I would do so,” Obama told the first group. “But we’re also a nation of laws. That’s part of our tradition. And so the easy way out is to try to yell and pretend like I can do something by violating our laws.”

Republicans accuse him doing just that.

In one of two policy memos issued earlier this month, U.S. Citizenship and Immigration Services announced that some immigrants from the 37 Visa Waiver Program countries who have stayed in the U.S. longer than allowed could apply to keep living here if they are immediate relatives of a U.S. citizen. People from those countries, mostly European allies, are allowed to visit the U.S. for up to 90 days without a visa.

The agency also announced that some immigrant parents, children and spouses of U.S. service members living in the country illegally would be allowed to stay.

Those moves stand in sharp contrast to the actions of Obama’s Homeland Security Department, which has deported nearly 1.9 million people during the president’s nearly five years in office, according to Immigration and Customs Enforcement data.

Advocacy groups have been as loud as the California protesters in calling for Obama to act while they maintain pressure on House Republicans with protests and acts of civil disobedience.

“House Republicans are infuriating, and legislation is the permanent solution, and we’re going to keep fighting for legislation. But that doesn’t let Obama off the hook,” Frank Sharry, executive director of America’s Voice, a pro-immigrant group, said Tuesday. “He continues to be the president who presides over record deportation.”

What angers the advocacy groups is that many of those deported are immigrants who would qualify for legal status or citizenship under the Senate-passed legislation, which Obama supports.

The organizations argue that Obama could expand his Deferred Action for Childhood Arrivals program, which dealt with some of the children brought into the country without legal permission, to their parents. He also could delay action against workers who have helped in the prosecution of employers who have broken the law or immigrants who don’t represent a threat to national security, the groups say.

“The president does have the authority and the ability to ease the crisis on the ground while the legislative process continues to play out,” Ana Avendano, director of immigration and community action at the AFL-CIO, said in an interview.

Advocates point to a June 2011 memo from Immigration and Customs Enforcement that provided guidance on using prosecutorial discretion in carrying out the nation’s immigration laws. The discretion applied to a range of steps that officers, agents and lawyers could take in enforcing the laws, such as deciding whom to stop and arrest or whom to release.

Advocates contend the memo gives immigration authorities flexibility to target only criminals for deportation but that the administration continues deporting noncriminals as well.

About 370,000 people were deported last year, down from more than 409,000 people in 2011. The Homeland Security Department received money to remove about 400,000 a year, but the government decides who those people are. Hirsoshi Motomura, a law professor and immigration law expert at UCLA, said Obama could decide, for instance, to provide deferred action to groups of people described as low priorities in previous discretion memos issued by former ICE Director John Morton.

Pablo Alvarado, executive director of the National Day Laborer Organizing Network, said in a statement that Obama has a “credibility gap” on immigration, imploring Congress to pass legislation while his administration implements its deportation policy.

“The president can do more, and he knows it,” Alvarado said.

Traveling with Obama in California, a White House spokesman, Josh Earnest, did not rule out more executive actions. That prospect unnerves Republicans who point to Obama’s unilateral changes to the health care law, such as delaying some requirements and enrollment deadlines.