(CNN) President Donald Trump suggested Monday that some adults had "grabbed" children at the Southwestern border to better their chances of entering the US while confronting federal agents during an incident Sunday that resulted in the use of tear gas.

Trump -- speaking at a roundtable event in Biloxi, Mississippi -- described what he called "grabbers" -- migrants who grab children and "think they'll have a certain status by having a child." He alluded to the people with children in the group as possibly not being their parents.

"In some cases, you know, they're not the parents," the President said. "These are people, they call 'em grabbers. They grab a child because they think they'll have a certain status by having a child. You know, you have certain advantages in terms of our crazy laws that, frankly, Congress should be changing."

When asked for evidence of his claim by reporters, Trump demurred.

"It's a term that's used because, as you know, many people, it's a very violent, horrible thing, that they feel they have an advantage when they're with a young child, and they call them grabbers," he said.

The term "grabber" has not been widely used.

In a statement Monday night, Homeland Security Secretary Kirstjen Nielsen said some members of the group are using women and children as "human shields."

"The caravan members are predominately male. It appears in some cases that the limited number of women and children in the caravan are being used by the organizers as 'human shields' when they confront law enforcement," Nielsen said. "They are being put at risk by the caravan organizers, as we saw at the Mexico-Guatemala border. This is putting vulnerable people in harm's way."

Customs and Border Protection Commissioner Kevin McAleenan told Chris Cuomo on CNN's "Cuomo Prime Time" that the Border Patrol chief on the scene said he had seen women and children standing in front of a group that was throwing rocks.

"He saw people throwing rocks right next to women and children," McAleenan said. "They did that, actually, behind members of the media as well. I have seen video of a scene where rock throwers are hiding behind camera people taking photographs of them while they are throwing the rocks. So it was a really dynamic, challenging situation that our agents tried to resolve as safely as possible and were really successful overall."

A group of migrants -- between 500 and 1,000, according to various estimates -- tried to enter the US illegally Sunday by breaching the border fence east of the San Ysidro border crossing near Tijuana, Mexico, according to McAleenan. McAleenan said Customs and Border Protection had to respond with force after men in the crowd began throwing rocks at the agents. Tear gas was used to repel the crowd.

Trump said at the roundtable that the tear gas fired on migrants at the US-Mexico border was "very safe."

Asked how he felt when he saw images of children and parents being tear-gassed, the President said his first thought was: "Why are they there?" He had falsely said earlier Monday that "we don't use it on children" after being asked if it was OK to use tear gas on children.

He said the substance was "a very minor form of the tear gas" and described it as "very safe."

"Why is a parent running up into an area where they know the tear gas is forming?" Trump asked. "And they're running up with a child?"

On Sunday, CBP used a form of tear gas called 2-chlorobenzylidene malononitrile, or CS. That's the tear gas the agency has used since 2010, during President Barack Obama's administration.

The National Center for Biotechnology Information describes CS as "a riot control agent which causes temporary irritation of the eyes and the mucosal surface of the respiratory tract." It is more potent than another chemical -- omega-chloroacetophenone, which is a primary component of mace -- "but less incapacitating," according to the center.

Sunday's incident was the first confrontation between Customs and Border Protection and the thousands of migrants who had been working their way toward Tijuana for weeks and had begun arriving in the border city. The incident led federal authorities to close the San Ysidro crossing, near San Diego, for several hours Sunday.

In a statement, a Customs and Border Protection spokesperson said the group had "ignored law enforcement agencies in Mexico" and assaulted US officers.

"Over 1,000 individuals who were part of the so-called caravan attempted to cross illegally into the U.S. by breaching sections of the fence and using vehicle lanes in and near the San Ysidro Port of Entry," the spokesperson said in an email statement. "This group ignored law enforcement agencies in Mexico and assaulted U.S. Federal Officers and Agents assigned to respond to the situation in San Diego. As a response to the assaults and to defuse this dangerous situation, trained CBP personnel employed less-lethal devices to stop the actions of assaultive individuals attempting to break into the U.S."

The spokesperson added, "CBP has been preparing for weeks for events like the one on Sunday. We have seen the use of violence by members of this so-called caravan who have attacked law enforcement personnel in Guatemala, Mexico and now the U.S. CBP will consider using all approved and available resources to protect travelers, caravan members and our agents and officers. CBP takes Sunday's employment of use-of-force very seriously. CBP reviews and evaluates all uses of force incidents to ensure compliance with policy."

Trump added that he wouldn't hesitate to close the US border -- and keep it closed -- if violence continues.

"We would close it and we'll keep it closed if we have a problem. And we'll keep it closed for a long time," he said.

Asked what would prompt the closure, the President said: "Violence. If they do a charge. Because with a closed border, it's very easy to stop."