President Trump stepping up threats Thursday - warning he might call up the U.S. military and shut down the southern border in order to stop a large group of migrants from reaching the United States.

In a series of tweets Thursday - Trump pointed a finger directly at Mexico: "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." Secretary of State Mike Pompeo is heading to Latin America on Thursday and is expected to meet with outgoing Mexican president Enrique Pena Nieto on Friday.

Trump's fiery threats - which include cutting off aid to the region - hasn't stopped the caravan from growing since it started heading north on Saturday.

Already into the thousands, the group has grown larger as more Hondurans defy their own government and join the trek making its way through Guatemala.

(SOUNDBITE) (Spanish w/ English translation) HONDURAN MIGRANT, CARLOS CASTELLANO, SAYING: "Through necessity and because of the economic crisis caused by the government, that is why we have to migrate." The migrants are crossing through the lush jungle - having to navigate through water - and challenging terrain - some overcome by heat during the long journey.

Others run from the police -who have tried to control the situation.

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(SOUNDBITE) (Spanish w/ English translation) GUATEMALAN POLICE OFFICER, FREDY BACHAN, SAYING: "We are regulating transit so that you all don't suffer any injuries." Despite Trump's threats to block aid to the region - the Guatemalan government is doing little to break up the caravan.

That country's president dismissing Trump's warning that financial help to Central America will be stopped if the caravan is allowed to continue.

Trump says halting this mass migration is even more of a priority than a new trade deal with Mexico.