SACRAMENTO — Gov. Jerry Brown said Wednesday that California would accept money from the Trump administration to beef up the state’s National Guard by 400 troops, but will not deploy service members specifically to the U.S.-Mexico border to stop undocumented immigrants from entering the country.

President Trump said last week that he wanted California, Arizona, New Mexico and Texas to send a total of 2,000 to 4,000 National Guard troops to the border, partly to stop a convoy of migrants from crossing into the country. The migrants, about 1,200 mostly from Honduras, had moved north into Mexico but largely disbanded there without approaching the U.S., although about 200 reportedly are expected to seek asylum in this country.

Trump’s proclamation April 4 deploying the National Guard said he had “no choice but to act” to ensure national security.

“With our current laws and resources, we cannot stop illegal aliens from crossing the border,” he said.

The Republican governors of the three other states promptly said they would comply, but Brown waited several days. When he answered, the response was nuanced.

“There is no massive wave of migrants pouring into California,” Brown wrote in a letter to Homeland Security Secretary Kirstjen Nielsen and Defense Secretary James Mattis. He said the California National Guard would accept federal funding to add 400 service members to fight transnational criminal gangs, human trafficking, and firearms and drug smuggling along the border and across the state.

“Let’s be crystal clear on the scope of this mission,” Brown wrote. “This will not be a mission to build a new wall. It will not be a mission to round up women and children or detain people escaping violence and seeking a better life. And the California National Guard will not be enforcing federal immigration laws.”

California now has 250 Guard members working throughout the state on efforts targeting gangs, smuggling and trafficking, including 55 who are stationed at the border.

Brown’s announcement straddled a line between accepting and rejecting Trump’s request. One expert noted that if the administration goes along with Brown, both sides could claim victory — California would gain resources to fight transnational crime in the state, and Trump could claim the state’s cooperation on an issue that at least touches on illegal immigration.

“He’s not absolutely rejecting the request,” said Louis DeSipio, professor of political science and Chicano studies at UC Irvine. “In the long run, it’s an untenable position for California to oppose the Trump administration on every policy.”

There were calls from fellow Democrats for Brown to reject Trump’s request outright.

State Sen. Kevin de León, whose SB54 sanctuary law minimizing local law enforcement’s cooperation with federal immigration agents is the target of a Trump administration lawsuit, said last week that Brown “should ignore Trump’s pointless and expensive call.”

The Los Angeles Democrat, who is trying to unseat Sen. Dianne Feinstein in this year’s elections, said Wednesday, “I appreciate that Gov. Brown has designed a clear and limited mission focused on real public safety threats — not phantom threats posed by women and children fleeing violence.”

There was no immediate response from the Trump administration on Brown’s request for money to pay for 400 new Guard troops. However, Homeland Security spokeswoman Katie Waldman said the governor’s efforts to help secure the border were welcome.

Nielsen and Brown spoke recently, Waldman said in a statement.

“She is pleased to have the support of all four border governors to help secure our Southwest border. Issues of border security require the partnership of the federal government and our state and local allies to be successful.”

At least one proponent of clamping down on illegal immigration said Brown needed to do more to keep California safe.

“Jerry Brown has just admitted that there are transnational gangs operating on the U.S.-Mexico border,” said Assemblyman Travis Allen, a Republican from Huntington Beach who is running for governor. “It’s necessary that we take steps to further secure our border to make sure that anyone coming into our state has been vetted and is coming through the front door.”

If the Trump administration approves California’s funding request, Brown would retain the ability to decline certain missions. It’s unclear how many of the new troops would be sent to the border. The memorandum outlining California’s conditions says the agreement would end Sept. 30.

Melody Gutierrez is a San Francisco Chronicle staff writer. Email: mgutierrez@sfchronicle.com Twitter: @MelodyGutierrez