There was new violence as Donald Trump brought his strict immigration policy to Mexico's doorstep.

The presumptive Republican presidential nominee campaigned Friday in San Diego, the busiest border crossing between the U.S. and Mexico.

Outside the convention center where he spoke was one of the largest protests organized against him.

About three-dozen people were arrested when anti-Trump demonstrators clashed with Trump supporters and police.

Reuters/Jonathan Alcorn

CBS News correspondent Carter Evans reports hundreds of protesters marched in the street near San Diego's convention center.

It began as a peaceful demonstration that included immigrant groups who disapprove of Trump's tactics and rhetoric.

"We're going to build a wall," Trump said to his supporters inside.

Outside, skirmishes erupted.

Police brought out their batons when some protesters tried to climb into a secure area where officers were monitoring the situation. At least one was arrested.

That led protesters to throw water bottles at the officers.

When the rally ended, the racially diverse crowd began exchanging angry words.

"Go back to Mexico," one man shouted.

Emotions boiled over, then things became physical.

"My friend was getting attacked by this guy," anti-Trump protester Jack Schwartz told Evans. "I pulled one guy off. The next guy comes in, socks me right here. Is my nose broken?"

In California last month, anti-Trump protesters burned an American flag and an effigy of the candidate. Sentiments continue to flare due in part to a large Hispanic population.

On Friday in San Diego, protesters also staged a sit-in.

"I don't agree with a lot of things that the presidential candidate Donald Trump has put out there," protester Judith Castro told Evans, "like the fact that he's using racism, discrimination."

As the rally began to wrap up, police in riot gear closed in on the crowd. They told people that it was an unlawful assembly and that everyone who remained there was there illegally and was subject to arrest.

Back inside, Trump continued his fight to take Calfornia despite claims that a Republican can't win the state.

"Honestly, folks, we have leadership right now in this country, especially at the top, that is grossly incompetent," Trump said. "They don't know what the hell they're doing."

During an appearance in Fresno earlier in the day, Trump waded into one of California's biggest problems, its historic drought.

In a private meeting with corporate farmers, Trump said, "There is no drought," and that he can fix the state's chronic water problems that pits rural water districts and well-off farmers against environmental laws.

"I've heard this from other friends of mine in California, where they have farms up here, and they don't get water," Trump said at a campaign rally. "I said, 'Oh, that's too bad. Is it a drought?' 'No, we have plenty of water.' I said, 'What's wrong?' 'Well, we shove it out to sea.' And I said, 'Why?' And nobody even knows why, and the environmentalists don't know why. Now, they're trying to protect a certain kind of three-inch fish."

Trump was referring to the Delta smelt, a native California fish that is on the brink of extinction.

Meanwhile, a debate showdown between Bernie Sanders and Trump appears to be off the table.

Trump said on Friday that it would not be appropriate for the presumptive Republican nominee to debate anyone but the Democratic leader.

Sanders is trailing Hillary Clinton in the race for the Democratic nomination, but he said he would still like to take on Trump.

"Trump goes around; he's a bully; he's a big, tough guy," Sanders told reporters. "Well, Mr. Trump, what are you afraid of?"

Trump initially said he would debate Sanders to raise money for charity but that no TV networks were ponying up.

The Sanders campaign said it received two offers from television networks.