While Mexican men travelling without relatives once made up the bulk of the migrants, Guatemalans and other Central Americans travelling in families or as unaccompanied minors are now the norm.
Since the mid-1970s, migrants from Central and Southern America have exploited Mexico's relatively lax policies on border security to enter the USA illegally. The rest would have to apply for refugee status or face deportation.
Mexican Foreign Relations Secretary Luis Videgaray said those with passports and valid visas would be let in immediately, though he acknowledged that "we anticipate those are the minority".
Any who decide to cross illegally and are caught will be detained and deported, the Mexican government has said.
Throughout the week, federal police aircraft arrived in the city of Tapachula, near the border with Guatemala, with hundreds of federal officers equipped with antiriot gear.
Mr Trump has made cracking down on illegal immigration a keystone of his presidency.
"I must, in the strongest of terms, ask Mexico to stop this onslaught - and if unable to do so I will call up the U.S. Military and CLOSE OUR SOUTHERN BORDER!" he wrote.
More Honduran migrants tried to join a caravan of several thousand trekking through Guatemala on Wednesday, defying calls by authorities not to make the journey.
Mexico's government has sought assistance from the U.N. High Commissioner for Refugees (UNHCR) to help process migrants claiming refugee status, which could help it to disperse the caravan.
He said the caravan is "not organic" and is being underwritten by political opponents of the Honduran leadership. On Thursday he threatened to close the U.S. border if Mexico didn't stop the caravan.More news: Bellinger leads off vs. Brewers in Game 5
The group of Salvadoreans, Hondurans and Guatemalans say they are fleeing violence and poverty.
One migrant said: 'One way or another, we will pass'.
"Honestly, I want to get to the states to contribute to that country, to do any kind of work, picking up garbage", he said.
Thousands of people and goods legally cross the US-Mexico border daily.
In the caravan, Central American migrants hiked from Honduras through muddy jungle and residential streets, some toting babies along with backpacks, Reuters images show.
This year's group began traveling from Honduras on October 13 and has swollen to 4,000.
On Thursday, Trump said he prioritizes border security over even the recently struck trade deal to replace NAFTA, the United States-Mexico-Canada Agreement, or USMCA.
Mexico's main reaction has been to step up security on its southern border with Guatemala.
Judicial Watch said terrorists can easily slip undetected into the caravan because minors are not properly vetted despite the fact many in Guatemala and Honduras have turned to criminal gangs committing violent crimes.
"The position of President Trump is the one he has always raised, I do not see him as anything surprising, I would be surprised by a different position", Ebrard told local radio station Radio Centro.
Military officials instructed troops to alert border agents if they encountered migrants, rather than intervene themselves, except in cases of self-defense.