Trump wants to send up to 4,000 troops to the border and has commitments for about 2,400 from those states and California.
California has rejected the Trump administration's initial plans for National Guard troops at the state's border with Mexico, arguing the work is too closely tied to immigration enforcement.
The Brown administration said Monday it's waiting for the federal government to sign the Memorandum of Agreement that California submitted last week.
Also a deputy assistant secretary at the Defense Department, Robert Salesses, claimed California has diminished to commit more than 200 troops to the campaign.
"California Governor Jerry Brown is doing the right thing and sending the National Guard to the Border". He said Homeland Security officials are "in continuing dialogue and discussion" with state officials and did not rule out an agreement on an even more circumscribed role for the troops.
Brown has been the only holdout among border state governors, as Texas, New Mexico and Arizona - all led by Republicans - moved quickly to send personnel. With increased manpower and funding in recent years, the Border Patol has seen the number illegal crossings. It is unclear at this point what specific jobs the troops would, or would not, perform at the border.
A California National Guard commander, Lt. Col. Tom Keegan, disputed that characterization, and said in a statement Monday that "state officials have not rejected anything".
Talks between US and California officials about the duties the California troops would perform soured Friday and over the weekend after state authorities told federal officials that they would not participate in vehicle maintenance and the other jobs outlined for an initial phase across the border in California, Arizona, New Mexico and Texas, the USA officials said. "It will be an iterative process".