President Trump declared America "full" on Friday as he warned illegal immigrants and asylum seekers to turn back from the southern border amid a surge in arrivals.

Trump traveled to the border with Mexico in California as part of a push to put border security at the heart of his 2020 reelection campaign.

He told a meeting of military officers and local officials: "Our country is full. Our area is full. The sector is full." Whether it was illegal immigrants or asylum seekers, the message was the same, he added. "Can't take you anymore. I'm sorry," he added. "Can't happen. So turn around. That's the way it is."

He also left open the prospect of closing the border with Mexico if the crisis continued, despite suggesting a day earlier that it was unlikely to occur.

"I'm totally willing to close the border, but Mexico the last four days have done more than they have ever done," he said.

His visit will include touring a section of recently rebuilt fencing that he believes will halt a surge in migrant families coming to the U.S.

At the same time, the White House published data reflecting the uptick in border crossings. It revealed U.S. Customs and Border Protection officers were called into action more than 100,000 times in March, the highest monthly number in more than a decade, it said.

Trump Friday received a hostile reception from California's governor.

"Since our founding, this country has been a place of refuge, a safe haven for people fleeing tyranny, oppression and violence. His words show a total disregard of the Constitution, our justice system, and what it means to be an American," said Gov. Gavin Newsom in a statement timed to coincide with the president's visit.