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More than a hundred Mexican federal officers carrying plastic shields abandoned a blockade they had formed on a bridge Saturday, allowing a caravan of thousands of Central American migrants to advance toward the United States.

At a news conference late Sunday, Mexican Interior Secretary Alfonso Navarrete Prida denied that his country's forces were responsible.

Stoking fears about the caravan and illegal immigration to rally his Republican base, Trump insinuated that gang members and "Middle Easterners" are mixed in with the group, though he later acknowledged there was no proof of that. Others were reportedly armed with guns and firebombs, but there's no indication that anyone on either side was actually shot.

Trump administration officials say they are still evaluating what to do if a migrant caravan arrives at the USA southern border.

Customs and Border Protection Commissioner Kevin McAleenan said Friday that the agency wasn't considering plans to have troops enforce immigration law. Some migrants rested in the shade of tarps strung across the town plaza, or picked up trash.

The tensions of a long trek, through searing heat and with tenuous supplies of food and other goods, spilled over Saturday night, when a dispute over a food line ended in a man's beating.

Most of the members of this caravan on Sunday postponed their departure from San Pedro Tapanatepec, in Oaxaca state, to reorganise their security measures after a fight occurred on Saturday night in which one person was injured.

Some hurled insults at the man with the megaphone, then they attacked him, Medina said.

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The assailants caught and beat him, but police intervened and he was treated at a hospital.

While such migrant caravans have taken place regularly over the years, passing largely unnoticed, they have received widespread attention this year with Trump's rhetoric. Kamala Harris made it sound as though it'd be un-American to turn the migrants away: "We are a country that - our strength has always been that we are a tolerant country, that we are welcoming, in particular, to those who have fled harm".

The group must travel about 75 miles (120 kilometers) to reach the border with Guatemala and another 185 miles (300 kilometers) to reach Mexico's southernmost border.

The trip could be twice as long if the 4,000 or so migrants head for the Tijuana-San Diego frontier, as another caravan did earlier this year.

A local official in southern Mexico says a disturbance broke out at the encampment of Central American migrants trying to make their way through southern Mexico toward the U.S. Only about 200 in that smaller group made it to the border.

The leaders of a caravan of Central American migrants making its way toward the US southern border called for its members to stop and rest near the Mexican town of Tapanatepec, about 1,000 miles from the USA border, The Associated Press reported.

"If something happens to you, someone will help you", said Jessica Yamileth Zabaleta Guzman, 24, who is traveling with her partner and their 1-year-old son. The IDs, called CURPs, authorize the migrants to stay and work in Mexico, and the ministry said pregnant women, children and the elderly were among those who had joined the program and were now being attended at shelters.