But many of Mr. Trump’s admirers were seeing something very different: the specter of the United States’ borders overrun.
Mr. Mujica was speaking by phone from Matías Romero, a town in the state of Oaxaca in southwest Mexico where the members of the caravan had spent the previous two nights, sleeping in a park.
The 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.
Alex Mensing, project coordinator for Pueblo Sin Fronteras, added: “We’re definitely not looking for some kind of showdown.”
Mr. Mujica predicted that at most 10 percent to 15 percent of the participants would seek asylum at the border. Most of the others would drop out along the way, many over the next several days as the group traveled from Oaxaca to the state of Puebla and on to Mexico City, and many of those would seek asylum or some other protection in Mexico.
In Puebla, Pueblo Sin Fronteras plans to hold workshops, led by volunteer lawyers, to teach migrants about their options for legal protections in the region, including in Mexico and the United States.
“We don’t promote going to the United States,” Mr. Mensing said. “It’s a challenging place to seek asylum.”
In recent years, Mexico has become an increasingly attractive destination in its own right, not just a passageway for Central Americans and others seeking sanctuary from economic hardship and violence in their home countries.
“We have a lot of people living in Mexico now,” Mr. Mujica said, speaking of participants in past caravans. “All they want is a place to live without fear.”
“We are trying — as Mexicans, as Americans — to find solutions,” added Mr. Mujica, a Mexican-American who holds dual citizenship.
In his Twitter posts on Sunday, Mr. Trump also asserted that many migrants trying to cross the border into the United States were seeking to “take advantage of” the program known as Deferred Action for Childhood Arrivals, or DACA, that has provided protected status to hundreds of thousands of young immigrants brought to the country as children. Mr. Trump announced last year that he was ending the program but was open to keeping it.
On Monday, advisers said that the president was also alluding to a perception, supposedly held by many Central American migrants, that as part of efforts to salvage DACA, Congress may soon agree to legislation that would permit unauthorized immigrants to remain in the United States.
But migrant-rights advocates, including coordinators of the latest caravan traversing Mexico, said these assertions were a White House invention.
“It’s laughable!” Mr. Mujica said. “Most of the people don’t even know what DACA is. They know that it’s almost impossible to get into the United States. They know that they’re deporting everyone.”
On Sunday, even Mexico’s secretary of foreign affairs, Luis Videgaray, weighed in, apparently in response Mr. Trump’s tweets that accused Mexico of lax immigration enforcement.
“Every day Mexico and the US work together on migration throughout the region,” he said on Twitter. “Facts clearly reflect this. An inaccurate news report should not serve to question this strong cooperation. Upholding human dignity and rights is not at odds with the rule of law. Happy Easter.”
Mr. Mensing said that the cross-country caravans originated in local protests inspired by the traditional Holy Week re-enactment of the Stations of the Cross.
Directors of migrant shelters and soup kitchens would conduct short, local marches along popular migration routes “as a way to highlight the kinds of things that would happen to migrants from Central Americans,” including kidnappings, sexual assaults and murders, he said.
In recent years, these demonstrations got increasingly ambitious. In 2014, a caravan left the southeastern Mexican town of Tenosique, in the state of Tabasco, with a plan to go to Palenque in the state of Chiapas. But the movement gathered momentum as it moved north and kept on going, Mr. Mensing said.
It was the first caravan to reach the United States border.
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