President Donald Trump made several misleading or false claims on immigration and the border on Monday, after defending his administration's use of tear gas on migrants attempting to gain entry to the U.S. over the weekend.

Here are his claims, made during a pair of campaign rallies and a law enforcement round table in Mississippi to bolster Republican Sen. Cindy Hyde-Smith in her runoff election, and the facts.

Claim: More than 500 'serious criminals' are in migrant caravan

"But I would say the violence is very strong. We have over 500 people that are serious criminals and gang members. And it’s a tough situation. We just don’t want that in our country. And we're keeping it in Mexico," Trump said at a law enforcement round table on Monday in Gulfport, Mississippi.

Trump's administration has made this claim before, but has yet to offer evidence or say how officials identified more than 500 alleged criminals within the caravan of Central American migrants traveling toward the U.S. border with Mexico.

Claim: Three border agents were badly injured

"We had tremendous violence — three Border Patrol people yesterday were very badly hurt through getting hit with rocks and stones," Trump claimed at the Gulfport round table.

That's false, according to the president's own administration. The Department of Homeland Security said Monday that there were no injuries during the weekend clashes in which border agents used tear gas against migrants seeking to enter the U.S.

Trump administration officials said the use of tear gas was justified because migrants were throwing "rocks and projectiles."

"Our Border Patrol agents and officers responded admirably and responsibly to the events on Sunday. It is a testament to their training and professionalism that no one was injured," DHS Secretary Kirstjen Nielsen said in a statement Monday.

Claim: My wall stopped the migrants

"The wall has started very, very substantially and in fact you saw the other day the wall stopped everybody and it was only the section that's now under construction. They've breached it but only momentarily, it didn't take long. Momentarily. That was called a very momentary breach," Trump said in the Biloxi rally.

This is misleading. Trump is currently repairing and replacing old border fence sections — just as previous administrations did — but he's not building any new sections yet.

Migrants who attempted to enter the United States illegally on Sunday — by trying to cross on either side of the San Ysidro Port of Entry at the border between Tijuana, Mexico, and San Diego — were stopped by tear gas, pepper spray and manpower, according to a statement from Customs and Border Protection and eyewitness reports.

Claim: 'Fake news' ignores crimes committed by immigrants

"In the state of Texas alone, according to the Texas Department of Public Safety, between 2011 and 2018, more than 663,000 crimes were committed by illegal immigrants. You know you hear these stories about 'oh they don't commit crimes, we commit crimes, they don't commit crimes. Oh, it's just us.' No, no, it doesn't work that way, it's fake news. It's fake news," Trump said in the Biloxi rally.

Trump is inflating the numbers here, according to statistics from the Texas Department of Public Safety. During that period, Texas data says there were 284,000 criminal offenses committed by people in the state that authorities knew were undocumented at the time.

Texas authorities estimate that about 270,000 undocumented immigrants were charged with crimes during this period. That's about 16 percent of the undocumented population in Texas.

Overall, there's no evidence foreign nationals or immigrants commit more crimes than Americans, which Texas' data specifically notes.

Claim: Democrats want to harbor violent criminals

“Yet Democrats want to abolish ICE. They want to turn America into one giant sanctuary city for violent criminals and MS-13 and other gang killers,” Trump said in the Biloxi rally.

Trump's claim about ICE is partly true, but requires some context, including that not all members of the Democratic Party are on board with calls to "abolish ICE." While some Democrats have advocated for eliminating or restructuring the Immigration and Customs Enforcement agency,none have advocated for ending immigration enforcement.

The second half of Trump's claim is entirely unsupported, as NBC News has fact checked previously. Democrats have not expressed or even hinted at a desire to encourage and support crime or gang members.

In addition, there's no evidence that sanctuary cities, which limit cooperation with federal immigration authorities, foster crime or gangs, and authorities have said sanctuary policies actually help them fight crime.

Claim: ICE is hunting down dangerous people

“Every single day, we are finding the illegal alien gang members and predators and throwing them the hell out of here, putting them in jail, or just plain getting them out of our country as nicely as possible,” Trump said in the Biloxi rally.

This is partly true. ICE does target undocumented immigrants deemed dangerous by law enforcement, arrest and deport them, but it's a small portion of their overall work. In fiscal year 2017, there were more than 181,000 arrests. Seventeen percent of those arrests were arrests targeting criminals, and 2.6 percent of the total were gang-related arrests. The rest were administrative arrests.

Claim: Obama separated families at the border, too

“Obama had a separation policy, we all had the same policy. I tried to do it differently, but Obama had a separation policy, but people don’t like to talk about that,” Trump told reporters before heading to Mississippi.

That's false. The Obama administration attempted to detain families together. It did not have a policy of family separation.