CIUDAD HIDALGO, Mexico - Thousands of Honduran migrants whose journey toward the United States has triggered a series of tirades from US President Donald Trump resumed their long march Sunday after crossing a river into Mexico.

Mexican authorities on Thursday had managed to block the "caravan" of migrants on a border bridge between Mexico and Guatemala, but many later forged a river below using makeshift rafts -- regrouping early Sunday to march north.

"No one is going to stop us, after all we've gone through" said 21-year-old Aaron Juarez, who was accompanied by his wife and baby and was walking with difficulty because of an injury.

"We are tired, but very happy, we are united and strong," added Edwin Geovanni Enamorado, a Honduran farmer who was part of the caravan, who said he was forced to leave his country because of intimidation by racketeering gangs. A federal police commander told AFP around 3,000 people were marching in the caravan on the Mexican side.

The caravan left San Pedro Sula in northern Honduras -- 700 kilometers (430 miles) to the south -- last weekend, following a call on social networks relayed by a former Honduran deputy. The caravan comprised around 4,000 people as it moved through Guatemala to the Mexican border, according to the Mexican government.

On Sunday morning, about a thousand migrants, including women and children, were still stranded on a border bridge hoping to enter Mexico legally via Guatemala. Mexican authorities insisted those on the bridge would have to file asylum claims one at a time in order to enter the country.

The authorities opened the border to women and children who were then taken to a shelter in the city of Tapachula, about 40 kilometers (25 miles) from Ciudad Hidalgo, Mexico. Throughout Saturday, around 900 migrants -- tired of waiting on the bridge -- resorted to crossing the Suchiate River below on makeshift rafts and police did not intervene as they clambered up the muddy riverbank on the Mexican side.

They are now heading to Tapachula, the next stop on a journey of at least 3,000 kilometers to the border between Mexico and the United States.

The caravan has triggered escalating anti-immigrant rhetoric from US President Donald Trump on Twitter. He has threatened to cut aid to the region, deploy the military and close the US-Mexican border if authorities did not stop the migrants.

At a rally on Saturday, he suggested the caravan was politically motivated.

"The Democrats want caravans, they like the caravans. A lot of people say 'I wonder who started that caravan?'" he said in Elko, Nevada, where the caravan has become an issue in the upcoming US mid-term elections.

Migrants denied their motives were political.

"We decided to join those who were going," said Edgar Aguilar. "This is not political. This comes from hunger, from the draught, it's for prosperity, for a better life. This is not political!"

"We are suffering for our families, for our children," Honduran Antonio Padilla said as he tramped toward the Mexican town of Tapachula on Sunday.

"They forced our children to work in gangs, they kill our kids if we don't obey." Another migrant, who gave his name as Jaled, said they were marching "because there is no work in Honduras, no education, nothing good. The cost of life increases every weekend."

Honduran President Juan Orlando Hernandez and his Guatemalan counterpart Jimmy Morales met on Saturday and condemned the march, saying it was "violating the borders and the good faith of the states."

The Honduran president admitted however that social problems were a contributory factor: "Without a doubt, we have a lot to do so that our people can have opportunities in their communities."

Guatemala has organized a fleet of buses to take Hondurans back to their country and by late Saturday 300 people had returned.

The migrants are generally fleeing poverty and insecurity in Honduras, where powerful street gangs rule their turf with brutal violence.

With a homicide rate of 43 per 100,000 citizens, Honduras is one of the most violent countries in the world, according to a Honduran university study.