White House "border czar" Tom Homan told CBS News on Monday "there's no intention to arrest" California Gov. Gavin Newsom, after President Trump suggested he was open to the idea — escalating a war of words over the protests and law enforcement response in Los Angeles.

"That whole thing's been taken out of context," Homan said. "They haven't crossed a line yet … If you cross that line, I don't care who they are — the governor, the mayor, whatever — and when you commit a crime against ICE officers, we will seek prosecution."

The administration and Newsom have sharply criticized each other over the handling of the Los Angeles protests, which were sparked by Immigration and Customs Enforcement actions in the city. Mr. Trump has accused Newsom of failing to deal with violence and ordered Marines and National Guard troops to the city. Newsom responded with a lawsuit over the troop deployments and argues Mr. Trump is inflaming the situation.

Homan has could be arrested if they are found to have impeded ICE. On Saturday, Homan didn't explicitly rule out arresting Newsom and Los Angeles Mayor Karen Bass in an interview with — though he didn't say arrests were coming, and said he doesn't believe Bass has "crossed the line yet."

Newsom later : "Come and get me, tough guy."

When about the idea of arresting Newsom, Mr. Trump said, "I'd do it if I were Tom," adding, "Gavin likes the publicity, but I think it would be a great thing."

But Homan told CBS News he'll "leave that up to" the Justice Department to determine whether anybody has impeded ICE. 

"There's no intention to arrest the governor right now. I don't know if he crossed that line," Homan said.

In the interview with CBS News, Homan said it "absolutely was" necessary to send National Guard forces into Los Angeles, saying protesters had caused property damage and assaulted ICE agents.

Newsom says the National Guard troops were illegally called up by the federal government without the state's permission, prompting a lawsuit Monday. Local officials argue the troops' presence could aggravate the protests, adding local law enforcement can handle the situation.

The administration has also activated 700 members of the Marine Corps to support the National Guard. Newsom's office : "The level of escalation is completely unwarranted, uncalled for, and unprecedented."