Only Border Patrol agents and other law-enforcement officers may apprehend drug runners and people attempting to enter the US illegally.
President Trump last week ordered National Guard troops to patrol the USA border with Mexico.
The one holdout border state is California, led by Democratic Gov.
In Arizona, the state Nationwide Guard launched it was boosting the number of troops it's going to ship to the border to 338 from 225. California Governor Jerry Brown has been at loggerheads with Trump over opposing stance on the United States' immigration policy.
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".
Trump administration officials have said that rising numbers of people being caught at the southern border, while in line with seasonal trends in recent years, require an immediate response. President George W. Bush sent 6,000 in 2006.
In Mexico City, a caravan of Central American migrants that had been heading north stopped in the Mexican capital.
"I worked with the Texas National Guard during their 2014 border deployment", Border Patrol Agent Hector Garza told Breitbart Texas in his capacity as president of National Border Patrol Council Local 2455. "He made a commitment when he ran for president and he's been adamant that he wanted to do everything he can to secure the border", he said.
"Ducey told a group of soldiers preparing to deploy from a Phoenix military base that their "mission is about providing manpower and resources" to support agencies on the border".
"I don't think this is a partisan issue or an identity issue", Ducey said.
Texan officials said about 300 troops would be dispatched, by the state, weekly until the complement of the National Guard reaches at least 1,000.
Abbott said on "Fox & Friends" that the decision will have a meaningful impact on border security, and that the proof can be seen by similar actions taken by former Presidents Bush and Obama.
There is no end date for the deployment.
Gov. Greg Abbott will meet with National Guard troops Thursday, days after they arrived in the Rio Grande Valley, according to a news release from the governor's office.
And those who serve say they would be honored to be a part of it.
South Carolina Gov. Henry McMaster, a Republican, provided to ship members of his state's Guard as correctly.