Trump, via his Twitter account said that if Honduras, Guatemala and El Salvador allow their citizens to enter the United States illegally, "all payments" to these countries will stop, adding that "anybody entering the United States illegally will be arrested and detained".
"He keeps the country mired in poverty and corruption", she said.
Police stopped the migrants at a roadblock outside Esquipulas for several hours in the afternoon, but the travelers refused to return to the border and were eventually allowed to pass.
About 160 people originally set off on Friday from San Pedro Sula, a notorious Honduran crime hotspot.
On Monday, Guatemalan authorities announced that they would prohibit the entry of the Honduran migrants if they do not comply with Guatemala's entry requirements.
On Tuesday, Pence tweeted that he had spoken with Hernandez, the Honduran president.
A migrant caravan set out on Saturday from the impoverished, violence-plagued country and was headed north on the long journey through Guatemala and Mexico to the USA border.
"Tell your people: don't put your families at risk by taking the unsafe journey north to attempt to enter the United States illegally", Mr Pence said.
A statement from the Foreign Ministry refers to the caravan as an "irregular mobilization" that is "obviously political and seeks to upset governability, stability and peace in Honduras and the United States".
Why did they leave Honduras?
Honduras suffers from high levels of violence, mostly attributed to powerful street gangs. Honduras is one of the most risky countries in the world to live in, while about two-thirds of the population lives in poverty.
Earlier in the day, Pence talked with Honduran President Juan Orlando Hernandez about the matter.
In Honduras, recriminations flew across the political aisle. "He has to take us in", said Andrea Fernandez, 24, who left Honduras with a newborn baby, a 5-year-old daughter, and 7-year-old son, because she said she couldn't find work and fears for their safety. The group was ultimately able to cross, said march organizer Bartolo Fuentes, a former Honduran lawmaker. "He has to take us in", she told the news agency. As local media documented the first steps of the group's journey over the weekend, government officials across the region spoke out, advising them to turn back.The US Embassy in Honduras warned of the dangers of the journey and noted that the United States would enforce its immigration laws. The group demanded "respect for the worldwide right to migrate and to seek asylum and refuge under domestic and global laws".
Mexico's migration institute said in a statement on Monday that march participants would have to qualify under immigration rules individually in order to pass through the country.
On Tuesday, Guatemala's Ministry of Foreign Affairs said that in response to the situation it would help the migrants now in their country, saying officials would carry out the necessary actions to "identify and document those who came into the country irregularly to the Guatemalan territory in order to regularize their migratory situation" and provide assistance with health, safety and protection.
"Migration is a human right", Hernandez said. "NEED WALL!", Trump tweeted at the time.