In addition to this original group, more than 1,000 migrants in a second caravan that forced its way across the river from Guatemala have begun arriving in the southern Mexico city of Tapachula.
President Trump made clear Thursday he will do everything in his power to stop them, dispatching extra troops, threatening to shut border entirely and saying in an afternoon press conference the military would consider rocks thrown at active troops "firearms". He later said that no migrants would be shot by the American military, but that anyone throwing rocks would be arrested.
The issue is being amplified by the president with less than a week before the midterm elections, and various sources have implied or stated without proof that Democrats and progressive donors are somehow funding the caravan that is composed of individuals and families fleeing dangerous conditions in their home countries in Central America. Others, including Mr Trump, have claimed — again, without proof — that the caravan includes "Middle Easterners". The president also indicated that he has no proof that Middle Easterners are in the caravan.
While numerous news outlets and watchdog groups have tried and failed to find proof for those claims — and none has been provided — Republicans clearly see a winning strategy in trying to tie Democrats to the caravan.
In the contentious Texas Senate race, for example, Senator Ted Cruz has attacked his Democratic opponent, Congressman Beto O'Rourke, and claimed that his campaign has been funding the migrant caravan. That statement was not substantiated with evidence that any of that financial support has occurred.
To see how the day unfolded, follow our live blog below.
Greetings from Washington DC, the nation's capital, where the nation's president is busily seizing on the issue of the migrant caravan - an act, critics say, intended to stir up his base ahead of the midterm elections. In a similar, anti-immigrant vein, the president has also threatened to end birthright citizenship and demand that only babies born into the US to parents in the country legally, have the right to citizenship
This is the story of a single mother from Honduras, Rose Gomez, who left her two children behind with their grandmother, to join the caravan. Here, she explains why she felt she had no alternative but to do so:
Under pressure from the US, Mexico has offered temporary work permits to migrants who register for asylum. The plan also envisages temporary ID cards, medical care and schooling but to qualify, migrants must remain in Mexico's southern Chiapas and Oaxaca states
The Associated Press said the caravan is currently in or around the city of Santiago Niltepec, which is located in the state of Oaxaca, and about 250 miles from the city of Oaxaca itself
Following Mr Trump proposal to end birthright citizenship, Republican senator Lindsey Graham says he will propose legislation in the senate that mirrors the president's plan, according to Reuters
Vice president Mike Pence is also supporting Mr Trump's plan, though no surprise there. He said the proposal may not conflict with the US constitution, despite what many experts say. "The Supreme Court of the United States has never ruled on whether or not the language of the 14th amendment, subject to the jurisdiction thereof, applies specifically to people who are in the country illegally,” he said in an interview with Politico
The AP now says the caravan is continuing its slow advance towards the Oaxaca state city of Juchitan, which was devastated by an earthquake last September.
Migrants along the highway on Tuesday have been stuffing themselves into truck beds and sprinting alongside semi-trailer rigs, trying to grab hold and pull themselves up, the news agency said
More than 1,000 migrants in a second caravan that forced its way across the river from Guatemala have now begun arriving in the southern Mexico city of Tapachula, the AP has reported. The first contingents began arriving to camp out in Tapachula's main plaza on Tuesday
Not all Republicans agree with Mr Trump's belief he has the right to end birthright citizenship. Speaker Paul Ryan said it was not possible to end birthright citizenship with an executive order. "You cannot end birthright citizenship with an executive order," Mr Ryan, the top Republican in Congress, said in an interview with radio station WVLK, according to the Washington Post.
Members of the latest caravan say they are not trying to catch up with the first because they believe it is too passive and they don't want to be controlled, according to Associated Press.
The first caravan of about 4,000 migrants, mainly from Honduras, passed through Tapachula about 10 days ago.
Donald Trump is currently visiting Pittsburgh following the deadly synagogue shooting. Members of Pittsburgh's Jewish community have been protesting the president's arrival.
"The gunman who tore apart our neighbourhood believed your lies about the immigrant caravan in Mexico," protest organisers said in an announcement. "He believed anti-Semitic lies that Jews were funding the caravan."
In a social media post, shooting suspect Robert Bowers accused the Hebrew Immigrant Aid Society (HIAS), a group that helps refugees, of bringing "invaders in that kill our people."
The protest announcement echoed an open letter from a group of local Jewish leaders who told Trump: "You are not welcome in Pittsburgh until you fully denounce white nationalism."
Good morning and welcome to our continuing coverage of the caravan of refugees and migrants making its way to the US-Mexico border.
President Donald Trump has started early this morning - repeating what has been a constant refrain over the last few days, that the military will stop the caravan.
Legally however, the military cannot detain, arrest or process anyone at the border - that must be left to Border Patrol agents.
Yesterday, Mr Trump expanded the issue of the migrant caravan to include "birthright citizenship" - the idea that anyone born on US soil is entitled to be called a US citizen.
In the greatest expansion yet of his hardline immigration policy, Mr Trump has claimed he will stop the practice, which is included in the 14th Amendment of the Constitution. He says it can be changed thanks to the wording of the Amendment, many legal scholars disagree.
