WASHINGTON — While President Donald Trump wavered Thursday on whether he will stop shielding from deportation people who were brought to the country illegally as children, his aides have identified at least two ways to end their protections without his fingerprints.

An executive order has already been drafted to end the program, Deferred Action for Childhood Arrivals, that allows hundreds of thousands of the immigrants to live and work openly in the United States. Trump used that legal mechanism to great fanfare to expand deportation authority and restrict entry to the country.

But with the president showing less willingness to sign such an order, advisers have begun to explore alternatives. Their hunt suggests that the White House is hesitant to publicly target a well-organized group of immigrants who have prominent public backing, including from former President Barack Obama, and to whom Trump has shown sympathy.

“DACA is a very, very difficult subject for me,” Trump conceded during a news conference Thursday in the East Room of the White House, promising to address the issue “with heart. … It’s one of the most difficult subjects I have because you have these incredible kids.”

Trump is caught between two camps. His supporters count the end of deportation protections as a key component of his promise to strengthen immigration enforcement. In campaign speeches, Trump repeatedly promised to end the program on “day one” of his presidency and called the protections “unconstitutional executive amnesty.”

On the other side, a mix of stakeholders, including the 750,000 people who have won work permits, want to see even more immigrants allowed to come out of the shadows. And some Republican strategists are concerned that suspending DACA could energize Latino voters and liberal activists in key congressional districts during the midterm elections next year.

“If he repeals DACA, people will start screaming at him,” said Alfonso Aguilar, a Republican strategist who heads the Latino Partnership for Conservative Principles and has advocated within the GOP for a path to legal status for people in the country illegally.

Senior Trump aides are holding fast to their goal of strengthening immigration enforcement, the president’s chief campaign promise. They have examined at least two options that would not directly involve Trump, according to two immigration policy advisers to the White House: a lawsuit brought by states and new legal guidance that details who is a priority for deportation.

Under that option, Attorney General Jeff Sessions would direct Justice Department lawyers to review the program, which issues two-year work permits to people who qualify and keeps them from being categorized as deportation priorities.

If the Justice Department determines that DACA is not legal or is no longer a responsible use of prosecutorial discretion, the Department of Homeland Security would be instructed to stop awarding and renewing work permits.

Another possible path involves the courts.

Some governors are considering a challenge patterned on the 2014 lawsuit filed by several conservative state officials against the Obama administration’s expansion of deportation protections. If they sue, Sessions could instruct his lawyers not to defend the program in court, exposing it to indefinite suspension by a federal judge.

Deportation relief could also be ended “the same way it was begun,” said Kris Kobach, the Kansas secretary of state and the architect of multiple state and local laws aimed at immigrants in the U.S. illegally.

Homeland Security Secretary John Kelly could simply instruct U.S. Citizenship and Immigration Services to stop issuing work permits, much as Obama’s first secretary of Homeland Security, Janet Napolitano, created DACA with a memo in 2012.

Trump has increasingly indicated he will not end the program, both at Thursday’s news conference and in private conversations over the last three months.

During their first post-election meeting at the White House, Obama nudged Trump not to start his presidency by attacking “Dreamers,” as the young immigrants are called.

Obama has said that if Trump targets Dreamers, he might speak out, a notable warning because Obama has said he’s otherwise reluctant to speak publicly on issues early in Trump’s presidency.

The White House is examining a range of options, an official said Thursday, saying no final determination has been made.

But some of Trump’s core supporters fear that the turmoil within the White House and the severe blowback from his travel bans are weakening the president’s resolve. His wobbling on the Dreamers, along with Republicans’ stalled attempt to repeal the Affordable Care Act, stand out as parts of Trump’s platform where pragmatic voices in the West Wing have quashed the rough-and-tumble impulses of Steve Bannon and Stephen Miller.

“It is worth giving them a little bit of leeway, but at the same time, you can’t really campaign on something being unconstitutional and then keep doing it,” said Rosemary Jenks, vice president and director of government relations for NumbersUSA, a group that advocates for reduced immigration levels.

Even though Jenks wanted to see DACA ended immediately, she was encouraged when Trump overhauled immigration law enforcement with an executive order signed in his first week that stripped limits on who should be deported. Now, about 8 million of the immigrants in the country illegally are considered priorities for removal, out of 11.1 million altogether.

“The Trump administration has done a lot to restore rule of law in immigration, and we are still in very early days, so I don’t think anyone should be criticizing them for not doing enough at this point,” said Kobach.

Washington Bureau’s Lisa Mascaro contributed.

brian.bennett@latimes.com