Washington DC - President Donald Trump said Tuesday that his Homeland Security chief Kristi Noem would remain in her job, despite a backlash over a fatal shooting by federal immigration agents in Minneapolis.

"No," Trump told reporters at the White House when asked if Noem would step down after 37-year-old nurse Alex Pretti was killed while protesting against immigration raids.

"I think she's doing a very good job," added Trump, in his first on-camera comments since the shooting on Saturday.

Melania Trump Melania Trump shifts blame on Minnesota protesters in call for "unity" after ICE killings

The New York Times reported that Trump held an almost two-hour meeting Monday evening with Noem, who has favored aggressive immigration raids and described Pretti as a "domestic terrorist."

The Republican president has also dispatched his border czar Tom Homan to Minneapolis, in a sign he may favor Homan's more targeted approach to the arrests of undocumented migrants over Noem's showy mass raids.

Trump, who was heading to Iowa to give a speech on the economy and affordability, continued his pivot from the White House's aggressive initial reaction to the shooting.

"I love his family, and it's a very sad situation," Trump said.

"We're doing a big investigation... I'm going to be watching over it, and I want to very honorable and honest investigation, and I have to see it myself."

Trump also further distanced himself from the comments by Noem, and by deputy chief of staff Stephen Miller, who called Pretti an "assassin" who wanted to murder federal agents.

The Trump administration says Pretti had a firearm with him, but video footage showed he was not holding it at any point in the confrontation, and that an agent had removed it before Pretti was shot.

"No," Trump replied, when asked if he agreed with Miller's comments.

"That being said, you can't have guns, you can't walk in with guns, you can't do that."

Zohran Mamdani Zohran Mamdani makes surprise appearance in Jimmy Fallon's Tonight Show monologue

Trump's comments look set to further inflame a debate about gun rights in the US sparked by Pretti's death.

His administration and law enforcement agencies under him have justified the fatal shooting on the grounds that Pretti had a handgun and accused him of acting violently when he became entangled with agents.

Some gun rights advocates – often staunch supporters of the president – have raised concerns over the Trump administration's comments about Pretti.

The Second Amendment stipulates that "the right of the people to keep and bear arms shall not be infringed." For decades, it has been the subject of intense controversy.