About 2,000 Central American migrants who circumvented Mexican police at a border bridge and swam and rafted across the river from Guatemala have decided to re-form their mass caravan and continue their trek towards the US.

The migrants, who said they gave up trying to enter Mexico legally because the asylum application process was too slow, gathered at a park in the border city of Ciudad Hidalgo.

They voted by a show of hands to continue north en masse, then marched to the bridge crossing the Suchiate River and urged those still on it to join them.

“We are going to reach the United States,” said Erasmo Duarte, a migrant from Danli, Honduras, despite warnings to turn back this week from US President Donald Trump.

A group of Central American migrants gather in the central park of Ciudad Hidlago
The migrants gather in Ciudad Hidalgo (Oliver de Ros/AP)

He has sought to make the caravan and border security in general into a campaign issue a little over two weeks before midterm elections.

The decision to re-form the migrant caravan capped a day in which Mexican authorities again refused mass entry to migrants on the bridge, instead accepting small groups for asylum processing and giving out 45-day visitor permits to some of them.

Authorities handed out numbers for people to be processed in a strategy seen before at US border posts when dealing with large numbers of migrants.

But many became impatient, and circumventing the border gate, swarmed across the river on rafts, swimming or wading in full view of the hundreds of Mexican police manning the blockade on the bridge.

Some paid locals the equivalent of 1.25 dollars to ferry them across the muddy waters.

They were not detained on reaching the Mexican bank.

A Honduras migrant is comforted by a Mexican paramedic
A young migrant is comforted by a Mexican paramedic (Oliver de Ros/AP)

“We couldn’t wait because we had already waited too long and they only told us lies,” said Mr Duarte, who joined the caravan with his wife and children six days ago.

Sairy Bueso, a 24-year-old Honduran mother of two, was another migrant who abandoned the bridge and crossed into Mexico via the river.

She clutched her two-year-old daughter Dayani, who had recently had a heart operation, as she got off a raft.

“The girl suffered greatly because of all the people crowded” on the bridge, Ms Bueso said.

“There are risks that we must take for the good of our children.”

Group leaders said the caravan, which will be smaller than the original one, would head for the city of Tapachula.

The caravan elicited a series of angry tweets and warnings from Mr Trump early in the week, but Mexico’s no-nonsense handling of the migrants at its southern border seems to have satisfied him more recently.

“So as of this moment, I thank Mexico,” Mr Trump said on Friday.

“I hope they continue. But as of this moment, I thank Mexico. If that doesn’t work out, we’re calling up the military – not the Guard.”

“They’re not coming into this country,” Mr Trump added.

“The Mexican government is fully engaged in finding a solution that encourages safe, secure, and orderly migration,” State Department spokeswoman Heather Nauert said, “and both the United States and Mexico continue to work with Central American governments to address the economic, security, and governance drivers of illegal immigration.”