"Someone has got to be a guide that tells [the president] that you either have the authority or you don't, or Mr. President, don't do it," Kelly said.
The retired four-star general shifted in his seat and looked away as Trump branded Germany a "captive" of Russia, but the White House says he was simply underwhelmed by the catering.
White House chief of staff says he spends up to eight hours a day in President Donald Trump's company.
Trump still seeks advice from his former aide, who stands accused of domestic violence.
The former general has questioned the role of the first daughter.
Jared Kushner and accused spousal abuser Rob Porter are among several staffers working at the White House without permanent security clearance.
"Problems start from the top and have to get solved from the top, and the president's the leader, and he's got to get everybody in a room, and he's got to lead," Trump once said.
Kelly made the remarks at a meeting on Wednesday with the Congressional Hispanic Caucus, according to Representative Ruben Gallego.
The chief of staff had said the congresswoman once claimed to have secured funding for the facility.
The Florida congresswoman struck back at General John Kelly calling her an "empty barrel," saying the attack is racist.
George W. Bush's ethics chief says Trump doesn't understand pain of military families because he "stayed home during Vietnam with his sore foot."
White House Chief of Staff Kelly has made efforts to keep his Marine son's death out of politics.
"The memo is less insane than one would have guessed," says a former Obama administration communications director.
The retired Marine Corps general was serving as Trump's homeland security secretary before being tapped for the White House post.
The Homeland Security secretary says heroin, cocaine and meth are bigger problems.
Director of Homeland Security also says people caught on airplanes when the new order goes into effect will be allowed into the U.S.