WASHINGTON — President Trump claimed Friday that ‘‘our country is full’’ as he tried to warn off migrants arriving at the southern border in increasing numbers, and threatened Mexico with automobile tariffs if the country doesn’t step up its efforts to curb migration from Central America.

‘‘Can’t take you anymore. Can’t take you. Our country is full. Our area is full, the sector is full. Can’t take you anymore. I’m sorry,’’ Trump said during a roundtable on the border at the US Border Patrol station in Calexico, Calif. ‘‘So turn around. That’s the way it is.’’

At the roundtable — which preceded a visit to the international border site in Calexico, a town of 40,000 people about two hours east of San Diego — Trump also continued to dismiss migrants’ claims of persecution, saying they were mainly gang members who had been coached by lawyers.

‘‘It’s a scam, OK? It’s a scam. It’s a hoax,’’ Trump said. Referring to the recently concluded investigation by Special Counsel Robert Mueller, the president added: ‘‘I know about hoaxes. I just went through a hoax.’’

Trump’s claim that the United States is ‘‘full’’ prompted pushback from his critics.

‘‘It’s just a ridiculous statement,’’ Representative Pramila Jayapal, a Washington Democrat, said in an interview shortly after the roundtable. ‘‘We have agriculture industries across the country that desperately need workers. We have construction industries in California and in other places that desperately need workers, and immigration has always been not just a question of immigration policy but who we are as a country.’’

Trump mixed fact with fiction when warning of the threat at the border. When complaining about the Flores legal settlement that governs treatment of migrant children and families, he blamed ‘‘Judge Flores, whoever you may be.’’ But Flores was an unaccompanied 15-year-old girl from El Salvador.

California and 19 other states that are suing Trump over his emergency declaration to build a border wall requested a court order to stop money from being diverted to fund the project.

Also on Friday, House Democrats filed a lawsuit preventing Trump from spending more money than Congress has approved to erect barriers along the southwestern border.

Trump has been increasingly exasperated at his inability to halt the swelling number of migrants entering the United States, including thousands who have been released after arriving because border officials have no space for them. Arrests along the southern border have skyrocketed in recent months, and border agents were on track to make 100,000 arrests or denials of entry in March, a 12-year high. More than half of those are families with children.

The rhetoric during Trump’s border tour Friday continued days of escalating threats to shut down the US-Mexico border, although he gradually backed off the pledge in recent days. His two-day trip to the West also included fund-raisers and a speech to the Republican Jewish Coalition this weekend.

Before leaving for California on Friday, Trump said he still ‘‘may shut it down at some point,’’ but that he was focused instead on issuing tariffs against automobiles from Mexico as a potential punitive measure. Since the threat, Mexico has been ‘‘absolutely terrific,’’ Trump said.

‘‘Mexico, I have to say, has been very, very good — you know that — over the last four days, since I talked about shutting down the border,’’ Trump said at the White House.

Hours before Trump touched down in Southern California, several hundred protesters gathered in the parking lot next to the border site, chanting anti-Trump slogans in English and Spanish while a balloon depicting the president as a baby flew overhead.

Speakers at the protest emphasized that people on both sides of the border were one community and that the agriculture sector couldn’t flourish without Mexican farmworkers. A small number of the president’s defenders — including about a half-dozen women wearing ‘‘Make America Great Again’’ hats — were also there, but dozens of police officers kept the crowd away from the border site Trump would visit.

‘‘Trump says Mexicans are rapists and criminals. That is wrong and cruel,’’ said Jesus Gonzalez, 43, of Calexico. ‘‘We don’t need his wall. We need a president with a heart and a brain.’’

Another demonstrator, Hildy Roberts, 22, said in Spanish: ‘‘We need a president who will listen to all the people.’’

Although about 650 miles of the US-Mexico is fenced off, no new border barriers have been erected during Trump’s presidency. Barriers in Calexico, which amount to a 30-foot-tall, 2.25-mile length of steel slats, replaced an existing fence.

Congress gave Trump about $1.375 billion in February to build 55 miles of new fencing, along the Rio Grande Valley area in Texas, although lawmakers restricted the construction to barrier designs that had already been deployed.

Material from the Associated Press was used in this report.