The migrant group left the southern Mexican border town of Tapachula on March 25, at that point numbering about 700. Most of the participants were from Honduras and many of them said they were fleeing violence and poverty in their home countries, organizers said. Some say they were inspired to flee Honduras following the violent suppression of political protests that erupted after last year’s presidential election.

Over the past week, the group grew in size, to about 1,200 by the time it arrived in Matías Romero.

But organizers said that contrary to the vision of a migrant onslaught on America conjured by Mr. Trump, most participants do not intend to travel as far as the border of the United States.

“He’s trying to paint this as if we are trying to go to the border, and we’re going to storm the border,” Mr. Mujica said.

Mr. Mensing added: “We’re definitely not looking for some kind of showdown.”

In an interview Monday, before negotiations between the Mexican immigration authorities and the caravan organizers began, Mr. Mujica predicted that at most 10 percent to 15 percent of the participants would seek asylum at the American border.

He said he expected many others to drop out along the way, especially if the caravan continued along its intended route through the state of Puebla and on to Mexico City, with some participants applying for asylum or other forms of protection in Mexico.

In Puebla, Pueblo Sin Fronteras plans to hold workshops, led by volunteer lawyers, to teach migrants about options for legal protections in the region, including in Mexico and the United States.