Brown last week had said he would accept federal funding from President Donald Trump to boost his state's National Guard.

But the governor has quibbled over their role and insisted they only focus on cross-border crime rather than detaining unauthorized migrants coming into the state that is home to several "sanctuary cities."

Ron Vitiello, the acting deputy commissioner of US Customs and Border Protection, said Brown had declined the initial roles put forward for Guardsmen.

"The governor has determined that what we have asked for so far is unsupportable," Vitiello told reporters.

"We've made this refined request, it's gone through the process and then we've got a signal from the governor that he is not participating."

Deputy Assistant Defense Secretary Bob Salesses said the initial request envisioned sending 237 Guardsmen to two main crossing areas in Southern California, where they would have conducted maintenance, clerical assistance and helped with heavy equipment operations, among other tasks.

"The California National Guard has indicated that they will not perform those missions as we know them to be right now," Salesses said, though he noted that conversations were ongoing.

Vitiello, too, suggested that the state's Guard might ultimately be used in other roles, including possibly cargo inspection.

"We will have other iterations," Vitiello said.

Trump this month said he would send thousands of National Guard troops to the southern border, where they could remain until a border wall is constructed.

The order would eventually see about 4,000 Guardsman along the border, which spans four US states.

So far about 960 have arrived, officials said. Texas has seen the biggest deployment, with 650 sent to the border, while Arizona has dispatched 250, and New Mexico about 60.

Vitiello said Guardsmen would most likely not be armed, but individual states might allow the carrying of a weapon in certain missions.

California is at the forefront of what opponents call the "Resistance" to Trump's administration, with the heavily Democratic state suing the federal government over numerous issues, including the rollback of environmental regulations.

Several cities including Los Angeles are "sanctuary cities" that require local law enforcement agencies not to tell federal agents about residents' legal status.

US Attorney General Jeff Sessions has sued the state over three statutes that support cities and counties that refuse to hand over unauthorized immigrants to federal immigration authorities for prosecution or expulsion.