The move came after President Donald Trump threatened to use military force to completely close the US-Mexico border over the issue.
"It was predictable, and it's also very close to the election", he said.
The migrants are fleeing their country because of violence and poverty. The US sent more than $175m (£130m) to the country in 2016 and 2017, according to the US Agency for International Development.
Earlier in the week, the U.S. president had threatened to cut aid to Honduras and send USA troops to the Mexican border. Hundreds of Mexican police officers in riot gear awaited the group of up to 4,000 would-be asylum-seekers.
Mr Trump has made cracking down on illegal immigration a keystone of his presidency.
Pompeo is scheduled to meet Fridaywith Peña Nieto and Foreign Minister Luis Videgaray, as well as Lopez Obrador's designated foreign minister, Marcelo Ebrard.
The caravan then began streaming toward a bridge that would take them to Mexico.
On Wednesday, the president also threatened to cut US aid to the Northern Triangle countries - Honduras, Guatemala and El Salvador - saying "all payments made to them will STOP (END)!".
Why does it concern Trump?
And the president-elect, Andrés Manuel López Obrador, has pledged to issue work visas for Central Americans in a bid to retain workers in the area rather than seeing them moving to the US. However, earlier this year Trump made a similar vow over another large migrant caravan, but didn't follow through and it largely petered out in Mexico.
This year's group began traveling from Honduras on October 13 and has swollen to 4,000.
The caravan itself has become a complex political symbol that some observers say is yet another ploy by rival Democrats and a hostile news media to portray the president in a negative light as the midterm elections approach.
"Nobody likes them (Trump's comments)".
Where is the caravan now?
Thousands of migrants have arrived at the Mexico-Guatemala border, with some climbing over the fence separating the two countries.
However, as USA Today notes, it is "not entirely clear" what Honduran President Juan Orlando Hernandez can do to turn the migrants back now that they are on Guatemalan soil.
Officials from the US and Mexico agreed on a plan of action in response to the approaching horde after President Trump threatened via Twitter to not only cut foreign aid funding, but to deploy the military to close the southern border as well.
He instead deployed the National Guard to the border.
And according to worldwide law, the USA can not deport asylum seekers without first determining the validity of their claim.
Pompeo is headed to meetings inMexico City with a message for leaders there about the massive caravan of migrants: Stop them before they reach the USA border.
Honduran migrants taking part in a caravan towards the United States, leave the Casa del Migrante (Migrant's House) in Guatemala City, Oct. 17, 2018. Mexico, however, requires a passport at entry.
"We hope that in this big caravan group, they let us in", he added, referring to the United States. Trump said in one tweet.
Mexican President-elect Andres Manuel Lopez Obrador, who takes office on December 1, wants to avoid repression against migrants and also avoid angering the United States.
"Well, we're looking at a lot of things", he said.
In Mexico, authorities say that any immigrant who crosses the border illegally will be deported.
On Wednesday, an advance group of exhausted migrants reached Guatemala City where they took refuge in a church-sponsored shelter.
But government statements, Twitter posts and even a police blockade haven't succeeded in stopping the caravan.
The region has one of the highest murder rates in the world.
He said the caravan is "not organic" and is being underwritten by political opponents of the Honduran leadership.