South Carolina Gov. Henry McMaster, a Republican, offered to send members of his state's Guard as well.
"This mission is about providing manpower and resources to support federal, state, county, tribal and local law enforcement agencies in stopping the flow of criminals, narcotics, weapons and ammunition that is being trafficked into our state", Ducey said.
Last Friday, Ducey announced that as many as 150 Guardsmen could be deployed to the border this week, but that number has now been upped to 338.
Those soldiers will be the first of an anticipated 250 from New Mexico serving in the border operation.
Despite drops in apprehensions of undocumented immigrants over time, Ducey said March saw a surge of unauthorized border crossings and illegal activity.
Although Homeland Security Secretary Kirstjen Nielsen has declined to indicate how long the operation might last, Trump said last week that he expected to keep the units "or a large portion of them, until such time as we get the wall".
"I don't think this is a partisan issue or an identity issue", he said.
Title 32 units typically act in law enforcement roles, but the Trump administration has said guardsmen in this deployment - as in previous deployments to the border under Presidents George W. Bush and Barack Obama - will be limited to support roles and will not be making arrests themselves.
The troops will not have law enforcement powers but will only provide support.
Nielsen and Defense Secretary James Mattis said in a joint statement late Friday that they had worked with the border-state governors to identify areas that guardsmen could address. Governor Doug Ducey says that is the name for the plan to deploy National Guardsmen to supplement the Border Patrol.
The New Mexico Guard members could help with air support, surveillance and infrastructure repairs, Hull said.
El Paso Sector Chief Patrol Agent Aaron Hull says those troops are nowhere near deploying yet.
California National Guard spokesman Lt. Col. Tom Keegan said last week that any request will be "promptly reviewed to determine how best we can assist our federal partners".
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. Yet, he acknowledged that the Bush and Obama administrations deployed far more National Guard soldiers, all with the same goal: To provide support for U.S. Customs and Border Patrol.
"You know, you don't want to say to people that are trafficking drugs and human beings across the border how long you're going to be there and show them a timetable", Ducey said.
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.
Ducey said that misstates what the soldiers will be doing.
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