The migrants plan to seek refugee status in Mexico or pass through to the United States, saying they are fleeing poverty and drug-fuelled violence in their countries.
"In Honduras there are no jobs, and the jobs that do exist aren't enough to live on", said Jose Francisco Hernandez, a 32-year-old from Copan state in western Honduras. About 150 of the 1,200 who began the month-long trek arrived at the southern US border in late April, according to The New York Times.
Some 1,300 people set off from northern Honduras on October 13, with some saying they'd be content being refugees in Mexico while others said they'd push for entry into the United States.
A day before the caravan formed, U.S. Vice President Mike Pence had urged leaders in Honduras, El Salvador and Guatemala to persuade their citizens to stay home and avoid the long, risky journey to the United States. Beginning in northern Honduras, they set foot across the southern Guatemalan border over the weekend after initially encountering a police blockade.
President Trump on Tuesday offered a fresh threat to cut off aid to Honduras if a large caravan of migrants continues heading toward the United States.
Of the caravan of migrants heading north, Piccolo said that America has consulates throughout Mexico that should work to stop the potential illegal immigrants - but expressed doubt Congress would act to help such a cause. Trump wrote on Twitter. Its travels were prominently covered Tuesday morning on "Fox & Friends", a program that Trump regularly views.
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Instead, Guatemala's government said in its own statement that it's now trying to identify and provide humanitarian assistance for the caravan.
Honduras is one of a dwindling number of countries that still have formal diplomatic ties with Taiwan, an island nation off the Chinese coast that Beijing views as a renegade province. During the meeting Pence reiterated that the USA was prepared to help with economic development and investment.
"What Trump says doesn't interest us", Fuentes said. The government of Mexico made a similar announcement.
Illegal immigration is likely to be a top issue in November 6 USA congressional elections, when Democrats are seen as having a good chance of gaining control of the House of Representatives from Trump's fellow Republicans.