President Donald Trump has said the US will "begin cutting off" foreign aid to Guatemala, Honduras and El Salvador because of a large convoy of migrants heading north.
Mr Trump criticised the countries on Monday for allowing people to leave the region and come "illegally" to the US.
The group is travelling through Mexico, but is still far from the US border.
Human rights organisations have said that cutting aid would make the situation worse.
The president has not specified what money will be cut and it is unclear if such action can be taken by presidential order.
In 2017, Guatemala received over $248m (£191m) in US aid. The same year, Honduras received $175m and El Salvador $115m, according to the US Agency for International Development.
"Cutting aid to refugee-producing countries will only make worse the conditions that displace people in the first place," said Human Rights Watch on Sunday.
The organisation said root causes must be addressed. "People generally don't want to leave their homes if they can live normal, safe lives there."
Though President Trump has accused the migrants of trying to illegally enter the US, many of the families travelling towards the border are seeking asylum.
They say they are fleeing persecution, poverty and violence in their home countries.
Why is President Trump reacting so strongly?
Curbing 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 Democrats in the House of Representatives.
Without offering evidence, Mr Trump has repeatedly suggested the caravan was politically motivated.
On Monday he urged people to blame Democrats for the border crisis, saying: "Remember the mid-terms".
Where are the migrants now?
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.
It is expected to take weeks before the caravan reaches the US-Mexico border, according to US media.
One of the closest border crossings in Brownsville, Texas is still over 1,000 miles (1,600 km) away from Tapachula.
The last leg of their journey will also have to wait until Mexico processes the group, and asylum claims can take up to 45 days.
Who are the migrants?
A group of about 1,000 Hondurans set off on foot from a bus terminal in the crime-ridden 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.
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.