Arizona, New Mexico, and Texas have pledged to send about 1,600 National Guard members to the US-Mexico border, responding to President Donald Trump’s plan to use the military to help fight illegal immigration and drug trafficking.

Texas governor Greg Abbott said he would add about 300 troops a week to the 250 members of the National Guard whose deployment was announced on Friday until the total number reaches at least 1,000 troops.

Arizona officials announced they were sending 225 National Guard members to the border on Monday and would deploy another 113 on Tuesday.

And New Mexico governor Susana Martinez’s office said that more than 80 troops would deploy later this week. They will be the first of an expected 250 Guard members from New Mexico to serve on the border.

Arizona, Texas, and New Mexico are all led by Republican governors. The other southwestern border state, California, is led by Democratic governor Jerry Brown and has not made a public commitment to sending troops from his state’s National Guard. Under the federal law Mr Trump invoked in his proclamation calling for National Guard troops, governors retain command and control over their state’s Guard members.

Mr Trump said last week he wants to send 2,000 to 4,000 National Guard members to the south-western border.

Arizona governor Doug 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 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”.

Mr Ducey initially said Arizona would send more troops on Tuesday but did not specify how many. The state’s National Guard in a statement later that 113 members would follow the initial deployment of 225.

Mr Ducey told reporters later that the deployments are needed to stop a surge of border crossings since March and accused the US government of previously ignoring the border “for nearly a decade”.

Texas agencies posted images over the weekend of Guard members arriving at the border. On Monday, Mr Abbott told San Antonio radio station KTSA that Texas will significantly ramp up its commitment to Mr Trump’s call over the next several weeks.

Some Guard members will be armed if they are placed in potential danger, Mr Abbott said. He added that he wanted to “downplay any notion” that “our National Guard is showing up with military bayonets trying to take on anybody that’s coming across the border, because that is not their role”.

He said that based on his conversations with Mr Trump and other officials, there is no end date on the deployment.

“We may be in this for the long haul,” he said.

Mr Ducey denied that his decision to send guard members to the border was politically motivated.

“I don’t think this is a partisan issue or an identity issue,” he said. “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 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.

Defence Secretary James Mattis last Friday approved paying for up to 4,000 National Guard personnel from the Pentagon budget through the end of September.

A Defence Department memo said the National Guard members will not perform law enforcement functions or “interact with migrants or other persons detained” without Mr Mattis’s approval.

It said “arming will be limited to circumstances that might require self-defence” but did not further define that.

The head of the US Border Patrol sector that includes part of West Texas and all of New Mexico said on Monday he met with leaders of the New Mexico National Guard to begin discussions about what will be required and their capabilities.

El Paso Sector Chief Patrol Agent Aaron Hull said those troops are nowhere near deploying yet. The New Mexico Guard members could help with air support, surveillance and infrastructure repairs, he said.