The closures of the pedestrian crossing and both the northbound and southbound vehicle crossings began around 11:30 a.m. Sunday after some members of the caravan tried to enter the United States through the San Ysidro Port of Entry's vehicle lanes, U.S. Customs and Border Protection officials said.
Trump has deployed military forces to the border to support the Border Patrol and threatened on Saturday to close the entire southern border.
But one Honduran man, who did not give his name, told AFP American officers had "got upset because we were close to the border".
Tijuana police said that 39 migrants have been arrested for participating in the unrest and causing disturbances.
About 5,000 Central American migrants have been staying at a sports center in Tijuana for more than a week.
President Donald Trump noted that some of the migrants continued waving the flags of their home countries even while trying to enter the United States, and said numerous migrants are "stone-cold criminals".
Adrees Latif Reuters
"Riot control agents are meant to temporarily incapacitate a person by causing irritation to the eyes, mouth, throat, lungs, and skin", the group said on its website.
He said he understands that the migrants want to be part of the United States, "but there's a legal way to do it". Vega issued a public appeal to Mexico's federal government to take over responsibility for sheltering the migrants and deport any who break the law.
He said officials were receiving more requests from migrants wanting to return to their countries, but did not have a number.
Tyler Q. Houlton, a spokesman for U.S. Department of Homeland Security, which oversees U.S. Customs and Border Protection, on November 26 tweeted that CBP "has always maintained the right to responsibly protect themselves from those wishing to cause them harm while they do their important and unsafe jobs".
President Donald Trump called on the Mexican government to do more to stop migrants approaching the US border, warning on Monday that he might permanently shut down entry if necessary. He tweeted as an example a 2013 article from the San Diego Union-Tribune saying border patrol agents used pepper spray against a group of about 100 migrants who threw rocks and bottles at agents. They only retreated when authorities deployed tear gas, which is said to have been felt almost a mile away.
Tear gas fumes were carried by the wind toward people who were hundreds of feet away, including some children. During his presidential election campaign, Trump promised he would have Mexico pay for the wall.
On Sunday, Mexico's Interior Ministry said that the country has sent 11,000 Central Americans back to their home countries since October 19. McAleenan said he was not aware of any successful illegal entries by caravan members into the US.More news: Chinese consulate in Karachi attacked by gunmen, 3 terrorists, 2 policemen killed