On Friday some tried to force their way across the frontier bridge, reportedly throwing rocks at riot police.
Among them was Osman Melgar, who nursed a bleeding gash on his shin, suffered when he fell as dozens of people packed on the bridge began fleeing when police, according to several eyewitnesses, used tear gas.
He told supporters at rallies...
These pictures capture the scenes unfolding on the Guatemala-Mexico border.
Throngs of people continued to wait on the bridge border crossing, where on Saturday morning many pressed for limited opportunities to plead their case to immigration officials, while many others opted to cross the river illegally, either on jury-rigged rafts or by swimming.
Some migrants at the Suchiate River border crossing, seized with uncertainty about their next moves, questioned whether so many had turned back.
Makeshift rafts carried some across the water, while others swam or waded. Hondurans were close behind with a 78 per cent denial rate, followed Guatemalans at 75 per cent.
The caravan, numbering anywhere from 5,000 to 10,000, is composed of young, unemployed men, women with children, some families and unaccompanied juveniles. Hundreds of migrants have reportedly applied for refugee status in Mexico in Ciudad Hidalgo.
China stays silent over killing of Saudi journalist Jamal Khashoggi
Saudi Arabia said on Saturday that Khashoggi was involved in "a physical confrontation, which resulted in his death". Saudi Arabia is also Germany's second-largest weapons customer. "So we have to use oil reserves", he said.
At the border bridge, a Guatemalan firefighter was pictured carrying a sick young boy.
Encamped for two nights using backpacks for pillows and tents made of trash bags on a long bridge between Guatemala and Mexico, the migrant caravan began in San Pedro Sula, Honduras, last week and grew exponentially as it passed through Guatemala.
Numerous migrants hail from Honduras, fleeing violence, poverty and a lack of jobs.
Hundreds of Honduran migrants decided on Saturday to cross the Suchiate River in their eagerness to reach the US.
The migrants are generally fleeing poverty and insecurity in Honduras, where powerful street gangs rule their turf with brutal violence.
Mexican President-elect Andres Manuel Lopez Obrador suggested Sunday that the United States, Canada and Mexico work out a joint plan for funding development in the poor areas of Central America and southern Mexico.
Authorities have given "priority attention to 164 women, 104 children and elders", the statement said, adding that some of the women are pregnant and there is at least one unaccompanied minor. He said he was recently deported from the United States after a brush with the law that he did not specify.
This is the second so-called "Migrant Walk" that has left Honduras this year in order to escape extreme violence and unemployment in a country that registered over 3,790 homicides in 2017 and seven percent unemployment, according to the Northern Triangle Mobility Initiative.
The migrants have defied threats by Mr Trump that he will close the US-Mexico border if the caravan advances, as well as warnings from the Mexican government that they risk deportation if they can not justify seeking asylum in Mexico.