All border traffic was halted temporarily on Sunday at a crossing between San Diego, California and Tijuana, in the Baja California state of Mexico, the US Customs and Border Protection agency said, Sputnik reported.
US President Donald Trump threatened on Saturday to close border checkpoints with Mexico, as a means of fighting illegal immigration.
"If for any reason it becomes necessary, we will CLOSE our Southern Border. There is no way that the United States will, after decades of abuse, put up with this costly and dangerous situation anymore!" Trump tweeted.
Trump reiterated in his tweets that only those already eligible for refugee status would be allowed into the United States.
The Washington Post reported that Mexican authorities had agreed to Trump administration's "Remain in Mexico" proposal. According to the proposal, migrants who wish to seek asylum in the United will stay in Mexico until a decision on their request is made.
On Tuesday, the Mexican Interior Ministry said around 5,600 migrants from Honduras, Guatemala and El Salvador were staying near the border cities of Tijuana and Mexicali. According to official figures, an estimated 2,600 migrants have settled near Tijuana.
The initial caravan of asylum-seeking migrants set out from Honduras in the direction of Mexico and the United States on October 13, hoping to gain refugee status in these countries. According to UN estimates, the caravan included more than 7,000 migrants. Another caravan of around 3,000 asylum seekers followed suit later in October.
Juan Manuel Gastelum, the mayor of Tijuana, said on Friday that he would not have city residents bear the burden of sustaining asylum seekers arriving from Central American countries in migrant caravans, adding that Tijuana was already suffering from a humanitarian crisis.
The White House in a cabinet order stated that deployed US troops will be allowed to "perform those military protective activities that the Secretary of Defense determines are reasonably necessary" to protect border agents, including "a show or use of force (including lethal force, where necessary), crowd control, temporary detention, and cursory search."
According to AP report, US agents have shot tear gas on Sunday at migrants after some tried to breach fence separating US and Mexico.