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WASHINGTON — The head of the U.S. Border Patrol on Monday could not rule out the possibility that some National Guard troops deployed to the U.S.-Mexico border might be armed for self defense, though troops deployed to date are unarmed.

Chief Ronald Vitiello told reporters that governors of border states would have the right to assess whether the troops in their states carry arms, particularly if they are on a mission that might require them to defend themselves.

"That's a case by case delegation, and that's determined by what the assignment is and most of the assignments won't require it. And then whatever the threat situation is, they'll be entitled to protecting themselves," Vitiello said at a news conference at the Department of Homeland Security.

Vitiello reiterated that no troops would be assigned to specifically arrest immigrants or do any kind of law enforcement work.

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The acknowledgment came moments after California announced it would not be sending troops to the border, as requested by the Departments of Defense and Homeland Security, because it considered the work to be too closely related to immigration enforcement.

"We are in continuing dialogue, discussion, with the California National Guard," said Robert Salesses, deputy assistant secretary for defense for Homeland Defense Integration.

Arizona, New Mexico and Texas have sent 250, 50 and 650 troops respectively, and the Department of Defense aims to grow that number to a total of 2,000 by the end of September, DoD officials told reporters.

The issue of whether or not to arm National Guard troops at the southern border is particularly sensitive because of the shooting death of an 18-year-old American citizen and goat herder by U.S. Marines who were patrolling for drug smugglers in the Rio Grande Valley in 1997. The killing sparked an uproar against the overuse of military force at the border.

President Donald Trump made a surprise announcement on April 4 that he would like to deploy the National Guard because illegal immigration over the southern U.S. border had increased to levels not seen since he took office.

At present, none of the troops who have been deployed are armed, the officials said. Their missions as of now are to provide intelligence through air surveillance and help with infrastructure projects at the border, but not to arrest immigrants, Salesses said.

He said cost estimates for the deployment are still being worked out. DoD will pay for the mission, but it is unclear whether the National Guard, the Army or another account will foot the bill.

Vitiello echoed Trump by saying the National Guard troops would remain at the border until they achieve "operational control."