President Trump - who earlier had threatened to stop aid to Central American countries - has warned Mexico in a tweet to "stop this onslaught", or he would call up the United States military and close the border.
The president told a rally of supporters that the "caravan" of migrants heading for the USA showed the need for stronger border protection after praising Mexico for sending riot police to its frontier with Guatemala.
He instead deployed the National Guard to the border.
"We are offering documented entry to those who have a passport and visa, and to those who do not, documented entry via an application for refugee status, on humanitarian grounds". One migrant said: 'One way or another, we will pass'. Later, he retweeted a video of Mexican federal police arriving at the Guatemalan border and wrote: "Thank you Mexico, we look forward to working with you!"
By Friday morning, at least a thousand migrants had arrived in the city of Tecun Uman, in northern Guatemala, and said they were preparing to cross into southern Mexico, even as Mexican authorities deployed additional police and Guatemalan officials shut a major border crossing.
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The group, consisting mostly of Honduran migrants, is making its way through Guatemala and hopes to continue northward through Mexico.
He claimed on Thursday that Democrats are backing the human movement to bolster their case for "open borders and existing weak laws".
Lopez Obrador wants to avoid repression against migrants and also to avoid angering the United States. In April, he said in a meeting with foreign leaders that the U.S.is "going to be guarding our border with our military".
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The Washington Post reported this week that Border Patrol agents arrested 16,658 family members in September, the highest one-month total on record and an 80 per cent increase from July, according to unpublished Department of Homeland Security statistics. There are no official estimates of the size of the group.
He posited that the Trump administration could coordinate with Mexico and Central American countries regarding the potential deployment of USA forces to aid as far as Mexico's border with Guatemala.
The Honduran Ministry of Foreign Affairs and International Cooperation urged citizens to stop participating in the caravan, as it could put their lives at risk. He also gleefully pointed out that Gianforte's assault may have helped him win his election.