Around 700 Marines are being deployed from their base in the Southern California desert to protect federal property and personnel, including federal immigration agents, US Northern Command said in a statement.
Trump has not invoked the Insurrection Act to allow the Marines and National Guard troops to carry out law enforcement duties. It is not clear if he intends to.
Los Angeles Police Chief Jim McDonnell said in a statement on Monday he was confident in his department's ability to handle large-scale demonstrations and that the Marines' arrival without coordinating with police presented a "significant logistical and operational challenge" for them.
California Attorney General Rob Bonta announced the planned lawsuit over the use of National Guard troops by telling reporters that Trump had "trampled" the state's sovereignty.
"We don't take lightly to the president abusing his authority and unlawfully mobilising California National Guard troops" Bonta said. He planned to seek a court order declaring Trump's use of the Guard unlawful and asking for a restraining order to halt the deployment.
The arrival of the National Guard followed two days of protests beginning on Friday after federal immigration authorities arrested more than 40 people across the city.
Crowds blocked a major freeway and set self-driving cars on fire as police responded with tear gas, rubber bullets and flash-bang grenades.
On Sunday, many protesters dispersed as evening fell and police declared an unlawful assembly. Some of those who stayed threw objects ranging from rocks to electric scooters at police and their vehicles.
Several dozen people were arrested throughout the weekend. One was detained for throwing a Molotov cocktail at police and another for ramming a motorcycle into a line of officers.
On Monday, thousands flooded the streets around City Hall for a union rally ahead of a hearing for arrested labour leader David Huerta, who was freed a few hours later on a $50,000 bond.
Huerta is the president of the Service Employees International Union California, which represents thousands of the state's janitors, security officers and other workers.
His arrest while protesting the immigration raids has become a rallying cry for people angry over the administration's crackdown.
Protesters linked hands outside the downtown federal detention centre where Huerta was being held, and refused police requests to move away. Religious leaders joined the protesters, working with organisers at times to de-escalate moments of tension.
Bonta accused Trump of fanning protesters' anger by the troop deployments, saying he set off Sunday's clashes. "This was not inevitable," he said.
Trump said Monday that the city would have been "completely obliterated" if he had not deployed the Guard.
Later, at a White House event, he added that state leaders "were afraid to do anything."
US officials said the full 2,000 National Guard members authorised by the president were expected to be on the ground by the end of Monday.
Other protests were taking shape across LA County, as confirmed reports of federal immigration agents in the cities of Whittier and Huntington Park south of Los Angeles spurred anger from activists. More protests were scheduled for cities across the country.
Governor Gavin Newsom urged Trump to rescind the Guard deployment in a letter on Sunday, calling it a "serious breach of state sovereignty."
The governor also told protesters that they were playing into Trump's plans and would face arrest for violence or property destruction.
"Trump wants chaos and he's instigated violence," he said. "Stay peaceful. Stay focused. Don't give him the excuse he's looking for."
The deployment appeared to be the first time in decades that a state's National Guard was activated without a request from its governor, a significant escalation against those who have sought to hinder the administration's mass deportation efforts.
