Sunday's incident happened after a group of migrants in the Mexican border city of Tijuana rushed at the border fencing.

It was the latest chapter in a saga that has pitted Trump's tough immigration line against thousands of migrants who have made their way north through Mexico from violent and impoverished Central American countries.

Tensions had been growing in Tijuana, and Trump said on Saturday the migrants would have to wait in Mexico until their individual asylum claims were resolved in the United States. That would be a significant shift in asylum policy that could keep Central Americans in Mexico for more than a year.

Read: U.S. Fires Tear Gas into Mexico to Repel Migrants

Trump went further on Monday, saying Mexico should send the Central Americans, mostly Hondurans, back home.

"Mexico should move the flag-waving Migrants, many of whom are stone cold criminals, back to their countries. Do it by plane, do it by bus, do it any way you want, but they are NOT coming into the U.S.A. We will close the Border permanently if need be. Congress, fund the WALL!" Trump tweeted.

Mexican government officials had no immediate response.

Mexico has been in negotiations with the United States over a possible scheme to keep migrants in Mexico while their asylum claims are processed.

U.S. government agencies defended the response to Sunday's incident at the San Ysidro crossing south of San Diego. News pictures showing children fleeing tear gas prompted sharp criticism from some lawmakers and charities.

British aid group Oxfam said in a statement the use of tear gas was shameful.

"Images of barefoot children choking on tear gas thrown by US Customs and Border Patrol should shock us to our core," Vicki Gass, Oxfam America Senior Policy Advisor for Central America said.

Democrats and other critics called the use of tear gas an overreaction, and questioned the idea of keeping the migrants in Mexico to make asylum claims there.

Some rights advocates and legal experts were concerned that the Trump administration was seeking to exploit the melee.

Geoffrey Hoffman, a professor and director of the University of Houston Law Center Immigration Clinic which represents migrants applying for asylum, said the government would use it to push the argument that the migrants should remain in Mexico.

Still, Rodney Scott, chief U.S. Border Patrol agent in San Diego, told CNN the vast majority of those assembled at the border were economic migrants who would not qualify for asylum, and said there were few women and children.

"What I saw on the border yesterday was not people walking up to Border Patrol agents and asking to claim asylum," Scott said, adding that authorities had arrested 42 people.

The U.S. Department of Homeland Security said U.S. Customs and Border Protection officers were struck by projectiles thrown by caravan members. U.S. officials reopened the San Ysidro crossing after closing it for several hours.

Donald Trump has said the migrants should not easily enter the country and on Monday he threatened again to shut down the U.S.-Mexico border, which stretches for 2,000 miles (3,200 km).

U.S. lawmakers face a deadline to approve funding for the federal government by Dec. 7. Trump has threatened to shut down the government unless Congress pays for his planned border wall.

REUTERS