Trump reacted with equal contempt toward another group that embarked on a similar journey to the southern US border in the spring, warning that none of the migrants would be allowed to cross.
Migrants who want to apply for refuge in Mexico were welcome to do so, they said, but any who decide to cross illegally and are caught will be detained and deported.
Photos showed the bridge between the two countries packed full of people, with many resorting to jumping in the river below after being blocked by Mexican riot police.
Though it began with just a couple hundred Hondurans headed for the United States, the support flowing in from leftist organizers and funders has grown this new caravan of hopeful immigrants into the thousands.
Mr Trump is returning to familiar territory by renewing his case for a wall on the southern United States border, a main theme of his 2016 presidential victory, even though... Late Thursday, some 300 Mexican federal police officers equipped with antiriot gear were deployed to the border crossing ahead of the caravan's expected arrival.
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However, by the end of Thursday, Trump was also thanking Mexico for its efforts to contain the caravan. Mexico has now requested that the United Nations High Commissioner for Refugees establish shelters along the border with Central America, a move both confirmed and welcomed by U.S. Secretary of State Mike Pompeo. If the Honduran President was more responsible, there wouldn't be so much emigration, but there are no jobs.
It's a strategy similar to what's been seen in US border cities when they became overwhelmed by large numbers of migrants.
Jari Dixon, an opposition politician in Honduras, tweeted on Monday that the caravan was not "seeking the American dream" but "fleeing the Honduras nightmare".
Central Americans traveling in a mass caravan broke through a Guatemalan border fence and streamed by the thousands toward Mexican territory Friday, defying Mexican authorities' entreaties for an orderly migration and U.S. President Donald Trump's threats of retaliation.
"So are you going to go back to that?"
"They are fully engaged, they sent 500 federales down to the southern border", Pompeo said, noting that he wanted to "express his sympathy" for the injured officers.
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Like Guatemala and Honduras, Mexico is a country of many migrants, raising the question of whether the political will exists for a confrontation.
It said the smugglers never crossed the border while they helped migrants over the wall in four places.
Mexican Foreign Minister Luis Videgaray insisted Mexico would not cave to pressure to detain the migrants, urging the Trump administration to address the root causes of their northward flight: violent crime and poverty.
Mexican President Enrique Peña Nieto has partnered with the United States in the past on immigration-related issues.
Members of the caravan - many with children in tow - gathered in the border city of Tecun Uman, Guatemala, Friday morning.
Pompeo said he and Videgaray spoke of the importance of stopping the caravan before it reaches the USA border. And if we go back to Honduras we'll suffer until the day we die.
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"Americans are compassionate people, and we empathize with all those who suffer and respect the desire of millions to become Americans".