Thousands of Central American migrants on Wednesday continued their 4,000-kilometre trek through Mexico towards the United States, albeit with fewer people than at the start.

"We are still in this fight," said organizer David Lopez as the bulk of the caravan reached Mapastepec, about 65 kilometres north of Huixtla, where the migrants had rested for two nights.

"Mexico has never seen a caravan of so many people," Lopez claimed.

The Mexican government on Wednesday estimated the number of participants at 3,600, down from a figure of 4,500 given on Tuesday. Organizers have put the number at 5,500.

The caravan left northern Honduras on October 13. Most of its participants crossed into Mexico illegally.

About 1,700 of them applied for refugee status in the country and stayed in Tapachula while their applications were being handled. But 110 of them later asked Mexico to help them return to Honduras, the government said.

About 170 migrants who had arrived in Huixtla also asked the local authorities to provide them with buses to travel back to Honduras.

Most of the migrants are Hondurans, although the caravan also includes nationals of Guatemala and El Salvador.

Migrants who travelled on from Huixtla said they felt the strain of the journey despite having rested and received food and medical care in the town.

"Until now, pretty tired," a migrant named Miguel Antonio told dpa. However, he added: "I think we can go on as before, the way we came."

The migrants were not yet sure which route they would follow to the US border.

"The caravan will not cross our southern border illegally under any circumstances," Secretary of State Mike Pompeo vowed on Tuesday.

Venezuelan officials meanwhile denied a claim by US Vice President Mike Pence that Caracas was financing the caravan.

Pence said on Tuesday that he had received the information from Honduran President Juan Orlando Hernandez, who had said the caravan was organized by leftist organizations and funded by Venezuela.

The South American country's President Nicolas Maduro on Wednesday said Pence's claim was laughable and called it "imperial paranoia."

"If it weren't for the fact that a crazy extremist like Pence said it and what it would mean for my personal safety... one would laugh," Maduro said during a meeting with supporters. "This laughable and worrying all at once."

The Venezuelan president added that he wanted to warn the world about Pence and the US government, which he claimed was "obsessed because they have not defeated us and they will not be able to defeat us."