El Salvador's leftwing government said it had solidarity with the migrants and respected their right to mobilize, but urged them not to risk their lives.
Trump has threatened to shut down the border with Mexico and last week said he would send troops.
More than a hundred Central American migrants have forced their way through a customs gate at the Guatemalan border town of Tecun Uman to request passage into Mexico.
Police commissioner Benjamin Grajeda said that authorities only blocked the highway Saturday to tell people about the offer. Those migrants clashed with Mexican authorities determined not to let the caravan grow or be repeated. Some fear they will be deported if they take advantage of the program.
The caravan is now trying to strike out for Tapanatepec, about 29 miles (46 kilometers) away.
Orbelina Orellana, a migrant from San Pedro Sula, Honduras, said she and her husband left three children behind and had made a decision to continue north one way or another. "We've thought about going before, but now we finally have the opportunity", said 18-year-old Dalila Abigail Landaverde, who is travelling with her partner and their three-year-old daughter, Tatiana.
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Back in 2013, the CDU had to make a coalition with the Alliance 90/The Greens after the election resulted in no clear victor . Of the SPD, he added: "A party on the way down can not suddenly rise from the ashes by going into the opposition".
"Our destiny is to get to the border", she said.
He said 1,895 had applied for refugee status in Mexico. The Mexican government is claiming that their police couldn't have killed the migrant because they were deployed without firearms "or anything that could fire rubber bullets".
Not long after the caravan resumed its advance Saturday, government officials lent them a hand.
Grupo Beta, Mexico's migrant protection agency, gave rides to stragglers and passed out water. The ministry said pregnant women, children and the elderly were among those who had joined the program and were now being attended at shelters.
Several mayors have rolled out the welcome mat for migrants who reached their towns - arranging for food and camp sites.
Several migrants, gathered by the capital's "Savior of the World" statue before leaving, said they were headed to the United States. Late Saturday night, groups of migrants were running through the town's streets saying a migrant's child had been snatched. Rojas transported the group to their destination after spotting them on a highway trudging through temperatures approaching 104 degrees Fahrenheit (40 degrees Celsius).
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Price responded by getting Justin Turner on a grounder to short and stranded Freese when Kiké Hernandez fouled out to Martinez". Los Angeles lost Game 7 of the World Series previous year to Houston, also at Dodger Stadium by the same 5-1 score.
At other times, police have ejected migrant passengers off buses by enforcing an obscure road insurance regulation. Mexican officials broke up a second, smaller group of 200 to 300, arresting more than 100 for deportation.
Homeland Security Secretary Kirstjen Nielsen, referring to USA troops who are expected to be deployed to the southern border to deter an incoming migrant caravan, said Thursday that "we do not have any intention right now to shoot at people". If they manage to catch up to the main body of the original caravan north of Tepanatepec they will no doubt blend into the massive crowd and disappear.
A larger group of thousands of Central American migrants has been winding its way through southern Mexico with the goal of reaching the US border.
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.
A caravan of migrants that left the Honduran city San Pedro Sula on Oct 13 has gained the attention of Mr Trump and other Republican politicians who have questioned the timing of the caravan just weeks before United States midterm elections on Nov 6.
U.S. Defense Secretary Jim Mattis announced that the military already has started delivering countermeasures to the southern border of the U.S., as Fox News previously reported.
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