Central American migrants making their way to the U.S.in a large caravan rest under a statue of Mexico's first Indian president Benito Juarez in Tapachula, Mexico, Sunday, Oct. 21, 2018.
The caravan elicited a series of angry tweets and warnings from Trump early in the week, but Mexico's initial handling of the migrants at its southern border seemed to have satisfied him more recently.
She added in a subsequent tweet that she has been in "constant contact" with her foreign counterparts in Mexico, Guatemala and Honduras, and that her department was monitoring the situation and ready to provide assistance if necessary.
Several hundred migrants had already applied for refugee status in Mexico and an estimate 1,500 were still on the Guatemalan side, hoping to enter legally.
They marched through Mexico and yelled slogans like "Si se pudo!".
As they passed through Mexican villages on the outskirts of Ciudad Hidalgo, they drew applause, cheers and donations of food and clothing from Mexicans. Others, meanwhile, waded into the Suchiate River or took rafts to get to Mexico.
"I believe Trump's heart may still be tender and one day he will feel peace and happiness and do good for us".
Footage showed the thousands of migrants walking down roads, many defiantly chanting "Yes we can" in Spanish as they pushed forward.
A business administration graduate, Lopez said she couldn't find work back home and hopes to reach the United States, but would stay in Mexico if she could find employment here.
Garcia said he had seen cases of swollen, lacerated and infected feet.
Throughout Saturday, around 900 migrants - exhausted of waiting on the bridge - resorted to crossing the Suchiate River below on makeshift rafts and police did not intervene as they clambered up the muddy riverbank on the Mexican side.
Mexican authorities accepted small groups for asylum processing and handed out 45-day visitor permits to others. Both leaders had spoken by phone with Pena Nieto and U.S. Vice President Mike Pence to discuss humanitarian aid and efforts to help people who want to return.
Mexican authorities on Thursday had managed to block the "caravan" of migrants on a border bridge between Mexico and Guatemala, but many later entered via a river separating the two countries.
Some, including 40-year-old Adriana Consuelo, paid raftsmen 25 pesos ($1.30) to ferry them across the river on vessels constructed of giant rubber tires. On the Mexican side of the bridge, they were met by Mexican police in riot gear.
Lopez Obrador also reiterated promises of jobs in Mexico for Central American migrants fleeing poverty and violence.
The migrants pose a challenge to Mexican President Enrique Pena Nieto's promise late last week to stop the travelers' plans to press ahead to the US border without the proper documents.
James tells NPR that people at the border say they'll do whatever is asked of them, as long as they aren't send back to Honduras.
However, the vast majority have opted to wait on the bridge over the Suchiate River where Mexican authorities insisted they would have to file asylum claims one at a time in order to enter the country. The number, however, may be misconstrued since people have been joining and leaving the caravan daily.
"Today it's for them, tomorrow for us", Valdivia said, adding that he was getting a valuable gift from those he helped: "From them we learn to value what they do not have".
Thousands of Honduran migrants resumed their march toward the United States on Sunday from the southern Mexican city of Ciudad Hidalgo.
Gerardo Hernandez, head of the local Mexican government's emergency services, confirmed to Reuters that more than 5,100 migrants were registered in three shelters in the Mexican border town of Ciudad Hidalgo.
Morales said a Honduran migrant died in the town of Villa Nueva, 20 miles (30 kilometres) from Guatemala City, when he fell from a truck.
More than 3,400 Hondurans migrants had been returned to their home country over the past 48 hours by Sunday afternoon, according to a migrant assistance body led by the wife of Honduran President Juan Orlando Hernandez, Ana Garcia de Hernandez.