But this particular caravan caught the attention of Mr. Trump, apparently after he heard about it on Fox News. In a Twitter tirade that began Sunday, he conjured up hordes of dangerous migrants surging toward the border. He demanded that Mexican officials halt the group, suggesting that otherwise he would make them pay dearly in trade negotiations or aid cuts.
Mr. Trump even boasted that his threat had forced Mexico’s government to halt and disperse the caravan participants. But there was no evidence of that on Wednesday.
Mexican migration authorities were distributing transit permits that would either give the migrants 20 days to leave the country or 30 days to formally apply for legal immigration status in Mexico.
Irineo Mujica, Mexico director of People Without Borders, an advocacy group that is coordinating the caravan, called Mr. Trump’s Twitter attacks and promise of a militarized border “campaign craziness.”
“There are 300 kids and 400 women,” he said. “Babies with bibs and milk bottles, not armaments. How much of a threat can they be?”
After making steady progress for a week through southern Mexico, the group has been bivouacked at the sun-blasted sports complex here since Saturday, before Mr. Trump started tweeting about it, surviving on food and water donated by residents in this rural town. They have slept on the ground, or in the bleachers of a soccer stadium, or under the roofs of a few derelict structures on the property.
A stream, shrouded by bushes and trees, is the latrine for the group, which once numbered about 1,500 but now hovers around 1,100, organizers said.
The caravan population has declined as participants have received travel papers and departed, though many of the hundreds who remain hope to continue moving north in a large group, which they do for safety from criminals.
Organizers said they were seeking buses or other transportation to move the migrants to the city of Puebla, about 250 miles away, to attend planned know-your-rights workshops on immigration law in Mexico and the United States.
The group, organizers and advocates said, represented a regional humanitarian problem, not a security crisis for the United States, as Mr. Trump has suggested.
“What he’s attacking is a supremely vulnerable population,” said Gina Garibo, projects coordinator in Mexico for People Without Borders.
Organizers also said their intent was never to storm the border, especially not with a caravan of this size. While the original plan included the possibility of escorting the caravan to the northern border of Mexico, organizers had expected the group to mostly dissolve by the time it had reached Mexico City.