Thousands of Central American migrants on Tuesday received food and medical care on their journey through Mexico towards the United States, while US President Donald Trump insisted there could be Middle Easterners in the caravan he does not want to let into his country.

Trump admitted there was no proof of people from the Middle East travelling with the Hondurans, Salvadorans and Guatemalans, but added: "There very well could be."

Trump's comments seemed designed to stoke up terrorism fears ahead of next month's mid-term elections.

The Mexican authorities estimate the number of migrants at 4,500 and organizers at 7,500.

The caravan left northern Honduras on October 13. Most of the migrants crossed illegally from Guatemala into Mexico and continued their journey despite warnings by the Mexican authorities that undocumented migrants would be deported.

Nearly 1,700 migrants so far have requested refugee status to legalize their situation, according to a government statement, while nearly 500 Hondurans have asked Mexico to help them return to their country safely.

The UN refugee agency UNHCR said the migrants included many who could qualify for asylum.

Migrants who sought refugee status stayed in the town of Tapachula, while others travelled northwards to Huixtla. They spent the night in the town and planned to continue resting to gather strength for the 4,000-kilometre trek to the US border.

The body of one of the migrants was found on the road linking the two cities, state prosecutors said.

The man, who was believed to have died from respiratory problems and dehydration, was the third casualty of the caravan after two others were killed when falling from moving vehicles.

Local authorities, churches and civil society groups attended to the migrants in Huixtla, providing them with medical care, food, water and clothes.

"We have created medical brigades, we have attended to a lot of boys, a lot of girls, a lot of women ... It is something that impresses you when you see it," Huixtla Mayor Jose Luis Laparra said.

Another caravan coming from Honduras, estimated to comprise about 3,000 migrants, was meanwhile expected at a migrant shelter in Guatemala City.

"I hope they manage to get through. We are demanding of the Guatemalan government that checkpoints be lifted," said Brazilian priest Mauro Verzeletti, director of the shelter.

About 30 Central American mothers whose children had earlier gone missing while trying to migrate meanwhile entered Mexico through the border post of Talisman.

Such caravans of mothers enter the country every year to search for their children.

In comments in the Oval Office, Trump said he had spoken with the border patrol many times and "they've intercepted many people from the Middle East," who included "good ones and bad ones."

He called Vice President Mike Pence forward to speak, who said Honduran President Juan Orlando Hernandez had told him that the caravan was organized by leftist organizations and funded by Venezuela.

Asked if the answer was to improve conditions in the migrants' home countries, Trump said that aid "hasn't worked for a long time in the countries."

"We have to focus on our country for a change," he added.

Secretary of State Mike Pompeo called the caravan an "unacceptable security risk."

The migrants were a "target for human traffickers who exploit them," he said at a news briefing.

"The caravan will not cross our southern border illegally under any circumstances," Pompeo vowed.