"Guardsmen will be sent to the border to provide mission-enhancing capabilities that will help U.S. Customs and Border Protection increase operational control of the region", an Arizona National Guard press release said of the first group of 225 Guardsmen.
New Mexico Gov. Susana Martinez's office said it would be deploying 250 guardsmen, including 80 later this week.
Rios said the added troops are unnecessary and that arrests at the U.S. -Mexico border are at an all-time low.
McMaster was one of Trump's earliest supporters in the 2016 Republican presidential primary but said there was nothing political about the deployment. The caravan had sparked furious criticism from Trump, adopted days later by his Nationwide Guard border security deployment plan.
"The Arizona National Guard will deploy 225 members of the Guard today to support border security measures", the state militia said in a statement.
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"This (deployment) isn't specifically around a border wall", Ducey said.
Arizona National Guard soldiers line up as they get ready for a visit from Arizona Gov. Doug Ducey prior their deployment to the Mexico border at the Papago Park Military Reservation Monday, April 9, 2018, in Phoenix. "You show me somebody who is for drug cartels or human trafficking or this ammunition that's coming over a wide-open and unprotected border here".
Mr Trump said last week he wanted to send 2,000 to 4,000 National Guard members to the border, citing "the lawlessness that continues at our southern border".
Defense Secretary James Mattis last Friday approved paying for up to 4,000 National Guard personnel from the Pentagon budget through the end of September. Instead, the governor told The Associated Press it was no different than other states sending troops to SC to help after a hurricane.
El Paso Sector Chief Patrol Agent Aaron Hull says troops are nowhere near deploying yet.
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The statement says the troops will help law enforcement agencies stem "the flow of trafficked people, criminals, narcotics, weapons, and ammunition trafficked in the state".
Mr Brown's spokesman, Evan Westrup, said California officials still were reviewing Mr Trump's troop request.
The Border Patrol said it caught around 50,000 people in March, more than three times the number in March 2017.
The National Guard has previously been deployed to help patrol the southern border, including in 2010 under former president Barack Obama, and from 2006-2008 under George W. Bush.
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