President Trump continued by saying ceasing the flow of drug and criminals into the U.S.is more important than global trade.
Honduran migrants bound to the U.S border climbed into the bed of a truck in Zacapa, Guatemala, Wednesday. Defense Secretary James Mattis later authorized the National Guard to deploy up to 4,000 troops on the southern border.
The Honduran government this week pleaded for the caravan to disperse, saying it was being used by political rabble-rousers to try to embarrass the US and Central American governments.
Trump, who ran in 2016 promising to tighten U.S. immigration laws end the inflow of people entering the country illegally, has called for cutting off foreign aid to Guatemala, Honduras and El Salvador if they do not stop the migrants.
"Later on, UNHCR could help the Mexican government to find places to settle (migrants) inside or outside Mexico for those granted refugee status, but that hasn't been defined with UNHCR yet", Videgaray told Reuters.
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.
"But we have also made very clear that there's no legal ground on which Mexico can issue a permit by which people can just go through Mexico towards the United States", he concluded.
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.
Media captionThe migrant caravan Trump keeps referencing Could Trump close the US-Mexican border? That means the arguments from the open-borders lobby that any migrants claiming any kind of dissatisfaction with their own countries have an affirmative right to asylum protections are flawed.
But Marcelo Ebrard, who has been picked as Mexico's next foreign minister, downplayed the comments and said Trump was appealing to his domestic political base.
Meanwhile, a Honduran caravan of migrants headed for the USA border has grown to 4,000.
Numerous more than 2,000 Hondurans in a migrant caravan trying to wend its way to the United States left spontaneously with little more than the clothes on their backs and what they could quickly throw into backpacks.
"A lot of money has been passing to people to come up to try and get to the border by Election Day", he said, without providing evidence.
US security experts, pointing to past history, say a lot of them are looking for jobs or to reunify with family already in the USA illegally, and aren't refugees.
As with a similar march in April, organizers of the march claim they will claim refugee status when they reach the us border with Mexico.
Guatemalan President Jimmy Morales on Wednesday dismissed threatened curbs to foreign aid, and said he had spoken with Honduran President Juan Orlando Hernandez about ensuring the migrants who want to return home can do so safely.