Transportation safety officers are set to be paid on Monday, but Tom Homan, the White House’s border czar, said ICE agents may stay where there are shortages.

Immigration and Customs Enforcement agents could remain at U.S. airports, where President Trump had sent them to respond to a shortage of security employees during a shutdown of the Department of Homeland Security, even after those employees are paid again, Mr. Trump’s chief border official said on Sunday.

“It depends how many T.S.A. agents come back to work,” the White House border czar, Tom Homan, said on CNN’s “State of the Union,” referring to the Transportation Security Administration. “How many T.S.A. agents have actually quit and have no plan coming back to work? I’m working very closely with the T.S.A. administrator and the ICE director to decide what airport needs what.”

Mr. Homan added later, in an appearance on CBS, that ICE agents would stay “until the airports feel like they’re 100 percent” and “normal operations” resume.

Mr. Trump signed an executive order Friday to pay T.S.A. employees as Congress remains at an impasse over funding the Department of Homeland Security.

Department officials have said about 50,000 T.S.A. officers should receive paychecks as early as Monday. But it is unlikely that pay will immediately alleviate operational challenges at the agency and at airports around the country.

More than 500 employees have quit, a department spokeswoman said last week, with wait times in security lines stretching for hours at some airports. She added that on Friday, more than 3,560 employees, over 12 percent of the agency’s work force, called in sick.

Mr. Homan contended on CNN that wait times had decreased since ICE agents arrived, doing identification checks and “plugging the security holes.” But their exact role has been unclear. The head of a union that represents T.S.A. officers said last week that ICE agents were “just getting in the way.”

Critics say ICE personnel at some airports are not carrying out tasks that would alleviate the burden of T.S.A. agents but rather patrolling halls or stationing themselves at checkpoints.

The standoff in Congress over funding the Homeland Security Department deepened on Friday, as House Republicans rejected a bipartisan deal and pushed instead to pass their own plan. They derided a Senate plan that would have funded most of the department but excluded money for Immigration and Customs Enforcement and Border Patrol, two agencies largely responsible for carrying out Mr. Trump’s deportation crackdown that have continued to operate under previously approved funds.

Senate Democrats have refused for weeks to fund the Homeland Security Department until the Trump administration agrees to guardrails on immigration enforcement after agents shot and killed two U.S. citizens in Minneapolis in January. Public anger over the incidents led to a scaling back of ICE’s presence in the city and changes at the Department of Homeland Security, including the replacement of Kristi Noem as its director.

There have been some reports of tension between ICE agents and travelers.

Last week, after a tip from T.S.A. led ICE agents to arrest a woman and her 9-year-old daughter at San Francisco International Airport, local police officers were called in to form a boundary between a growing crowd and the agents escorting the family. They were later deported to Guatemala.