Under the federal laws Trump invoked in his proclamation calling for Nationwide Guard troops, governors who ship troops retain command and administration over their state's Guard members and the US authorities picks up the value. On Friday, Defense Secretary James Mattis signed a memo approving U.S. Department of Defense funding through September for up to 4,000 troops along the border. The troops were sent to the town of Marana, northwest of Tucson, according to Ducey's spokesperson, Patrick Ptak.
South Carolina Adjutant General Robert Livingston says details including how many troops the state will send, their duties and how long they will stay will have to be worked out. They also would not be armed unless necessary for self-protection.
Grijalva said the border is one of the safest places in the state and border crossings are at a 45-year low.
But Abbott said he wanted to "downplay the notion" that the National Guard would be "trying to take on anybody that's coming across the border".
Officials planned to deploy 225 Arizona National Guard troops from Phoenix on Monday.
The country's Senate passed a resolution last week saying Mexico should suspend cooperation with the USA on illegal immigration and drug trafficking in retaliation for Mr Trump's move.
Trump talked about last week he wishes to ship between 2,000 and 4,000 Nationwide Guard members to the border, issuing a proclamation citing "the lawlessness that continues at our southern border". The caravan had sparked furious criticism from Trump, followed days later by his National Guard border protection deployment plan.
The troops will not have law enforcement powers but will only provide support.
Brown has repeatedly fought with Trump over immigration policy.
Grijalva said deploying troops send the wrong message to Mexico and to America.
The Arivaca area rancher says that in recent months she's seen an increase in the number of undocumented immigrants coming across her land. That would be larger than when President Obama deployed 1500 troops and smaller than President Bush's deployment fo 6000. California National Guard spokesman Lt. Col. Tom Keegan said last week that the request would be "promptly reviewed to determine how best we can assist our federal partners". New Mexico's Republican governor has said her state will take part in the operation, but hasn't announced a deployment.
"These Guard troops are there to support the Border Patrol".
"The state of Arizona must not be used as a political pawn that will leave visitors questioning the safety of our state", he said in his letter to Ducey.
Trump has said he wants to use the military at the border until progress is made on his proposed border wall, which has mostly stalled in Congress.