Trump also suggested that the migrants hoping to enter the USA are linked to crime and drugs that he said are "pouring in", and he called on Mexico to stop the "onslaught".
Trump also said that if a solution is not found, it could upend the new trade deal negotiated between Mexico and the United States.
Vaughan also pointed out that Guatemala has already caved into the caravan, but she is encouraged that Mexico has deployed officers to its southern border. Meanwhile, the State Department is attempting to stave off that possibility by compelling the Mexican government to stop them at their border with Guatemala.
Hundreds of other members of the caravan who are lagging behind are expected to join the group that is gathered at the border.
Shelters and churches along the border have been flooded as a result of the surge as U.S. Immigration and Customs Enforcement agents have been releasing hundreds of migrants from detention at a time.
Mexico's government says migrants with proper documents can enter Mexico and those who don't either have to apply for refugee status or face deportation.
At the established shelters, United Nations officials will vet the refugees to decide which ones have legitimate claims for refugee status, the official told Fox News. And former Presidents George W. Bush and Barack Obama both deployed National Guard troops to the border during their administrations to bolster security.
It was not immediately clear what form of military deployment Trump had in mind.
Mexico's Ambassador to Guatemala, Luis Manuel Lopez Moreno, met with leaders of the caravan Wednesday and warned them that Hondurans caught without papers in Mexico would be deported.
Recent U.S. efforts to curb immigration have come as record numbers of families have sought to enter the United States, although the overall number of people crossing the border is much lower than in previous years.
Mike Pompeo, the secretary of state, is travelling to Mexico City and expected on Friday to meet Mexico's president, Enrique Pena Nieto, to discuss the situation, as Mexico scrambles to dissuade the migrants from entering its territory.
So, for the time being, worldwide law will continue to be used as a blunt instrument to trash the Trump administration's immigration agenda, even though the U.S.is more than meeting its global legal obligations. "All Democrats fault for weak laws!"
Washington has committed $2.6 billion in assistance to the Northern Triangle countries of Central America - Honduras, Guatemala and El Salvador, all of which are the source of many migrants.
"Well, we're looking at a lot of things", he said.
Juan Escobar, 24, who was among the Honduran migrants in the caravan, said such rhetoric would not dissuade them from continuing the journey.