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Thousands of people travelling from Central American nations to try to enter the US have resumed their journey from southern Mexico to the US border.
On Sunday, the migrant caravan reached the town of Tapachula, approximately 37km (23 miles) from Mexico's southern border with Guatemala.
The Mexican authorities had earlier tried to stop them at a border bridge.
But some managed to cross into Mexico illegally by boat over the Suchiate river.
"We have sunburn. We have blisters. But we got here. Our strength is greater than Trump's threats," migrant Britany Hernández told AFP news agency.
US President Donald Trump has repeatedly warned the migrants to turn back, threatening to close the US border and cut aid to countries allowing the caravan to pass.
In tweets on Sunday, he said efforts were being made to "stop the onslaught of illegal aliens".
He also suggested the caravan was politically motivated. "The Caravans are a disgrace to the Democrat Party. Change the immigration laws NOW!'" he said.
Limiting illegal immigration was one of the main campaign promises Mr Trump made when he ran for president.
His Republican Party is facing mid-term elections on 6 November and could be unseated by the Democrats in the House of Representatives. With 15% of all voters saying that immigration is the most important issue facing the US, a caravan of migrants heading towards the US is the last thing the president wants.
A group of about 1,000 Hondurans set off on foot from a bus terminal in the crime-ridden Honduran city of San Pedro Sula on 13 October in an attempt to escape unemployment and the threat of violence.
Many of them had become aware of the caravan after a former lawmaker had published a poster announcing the caravan on Facebook. News of it quickly spread on social media.
One mother of two told Honduran newspaper El Heraldo that "it's our dream to reach the United States, we want to give our children a better future and here [in Honduras] we can't find work".
They have since been joined by other Central American nationals as they crossed Guatemala towards the Mexican border.
The region has one of the highest murder rates in the world and many try to flee gang violence.
Migrant caravans of this scale are a recent phenomenon. While Central Americans have long fled their homelands for the US and have sometimes joined forces along the way, the organised nature of these caravans is relatively new.
There are many danger along the way and many migrants think travelling in a group will be safer
This is the second such caravan to leave Honduras this year. A similar convoy reached Tijuana on the southern border of the US in April after travelling 3,500km (2,175 miles).
That march was organised by a rights group calling itself Pueblo Sin Fronteras (people without borders) which says it is trying to draw attention to the plight facing the migrants at home and the dangers they run during their attempts to reach safety in the US.
For the migrants, especially the most vulnerable ones such as the elderly and mothers with small children, the caravan offers more security than setting off on their own.
Migrants are often kidnapped by people traffickers and drugs gangs who force them to work for them. A large group is harder to target and therefore offers more protection.
The exact number is hard to determine as the group has split up. Some are already in the Mexican city of Tapachula while others are still at the Guatemala-Mexico border.
The caravan has been growing in size with more people joining along the way
Some estimates put the number of migrants who left Ciudad Hidalgo for Tapachula on Sunday at 5,000 while a Mexican federal police commander gave a lower number of 3,000. Another 1,500 migrants are estimated to be waiting to cross at the Guatemalan side of the border.
A newly formed group of 1,000 mainly Honduran migrants has also set off for the US.
Threatened with having US aid cut off, Honduran President Juan Orlando Hernández urged citizens not to join the caravan. His country has also sent buses to the Mexico-Guatemala border to repatriate those who may have changed their minds about heading to the US or who are simply too exhausted to carry on.
According to official figures, 3,400 Hondurans who had formed part of the caravan have returned to their homeland.
Mexico said it would stop those who did not have passports or the correct visas at its southern border. But faced with thousands of migrants and after initial clashes, riot police got back on the buses that had brought them to the border bridge.
About 900 migrants crossed the river and made it into Mexico, without the police intervening.
Mexican officials say they have been encouraging the migrants to apply for asylum and that more than 1,000 have started the process, which can take up to 45 days to complete.
Those who managed to cross into Mexico expressed their joy at having it made that far. Many shouted "Yes, we could!" and "we won't stop".
"We're exhausted, it's been a terribly difficult journey but we have hope: we've made it to Mexico, which means a lot to us," a migrant called José Luis told BBC Mundo.
A woman called María, who is taking part in the caravan with her husband and her two small children, told BBC Mundo's Ana Gabriela Rojas: "We are very happy to be here and we ask Mexican authorities and people to let us pass through. We are just looking for a job and better living conditions."
Carlos, a migrant who was walking at a fast pace, said that he feared being deported. "It's better to keep walking fast," he said.
