The Pentagon significantly escalated the federal response to the immigration enforcement protests in Los Angeles on Monday, mobilizing a battalion of 700 Marines and doubling the number of California National Guard troops in what officials described as a limited mission to protect federal property and agents, even as President Trump described the situation as “very well under control.”

Earlier Monday, Mr. Trump labeled the demonstrators “insurrectionists,” but he stopped short of saying he would invoke the 1807 Insurrection Act, which would allow him to call up the military to intervene directly in putting down the protests.

In an announcement, the Pentagon did not make clear why it would need an additional 2,000 National Guard troops. But more worrying to state and city officials, legal experts and Democrats in Congress was the use of active-duty Marines. By tradition and law, American military troops are supposed to be used inside the United States only in the rarest and most extreme situations.

The mystery was deepened by the fact that the president said the unrest was calming down thanks to his decision to federalize the California National Guard and send its troops into the streets, over the objections of Gov. Gavin Newsom. On Monday evening, the state filed a federal lawsuit challenging the Trump administration’s move and calling president’s actions illegal.

In a statement on Monday night, Sean Parnell, a Pentagon spokesman, said the decision to send the additional National Guard troops was made “at the order of the president.”

The mixed messages — Mr. Trump’s flexing of additional military power in response to the protests, even while claiming early success — came after several days in which the president and his allies have appeared to relish the immigration standoff with local and state officials.