Thousands of Central American migrants, primarily from Honduras and Guatemala, headed north through Mexico toward the U.S. on Sunday, brushing past efforts by Mexican authorities attempting to stop their advance at the border.

President Trump has threatened to stop aid to Honduras and Guatemala and shut down the border with Mexico if the migrants are allowed to reach the U.S.

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Mexican President Enrique Pena Nieto has pledged that Mexico would register the migrants and process requests for asylum. Those attempting to skip the process would face deportation, but the size of the caravan will test Mexico, which has sought help from the United Nations to manage the issue.

The migrant caravan began in San Pedro Sula, Honduras, last week and grew steadily as it made its way Guatemala. Estimates of their numbers Sunday varied between 5,000 and at least 7,200.

Many of the migrants have said they gave up trying to use the legal process to enter Mexico because the process was too slow. Mexico’s Interior Department said it had received just 640 refugee requests by Hondurans in the caravan. Many of the migrants who grew impatient worked their way around a border gate and crossed into Mexico. The caravan has been shadowed by Mexican authorities but have so far not been stopped.

It is unclear what the Mexican officials will do should the caravan reach the U.S.-Mexican border. Trump administration officials have said they are counting on Pena Nieto's government to address the situation. Secretary of State Mike Pompeo met with Pena Nieto in Mexico City on Friday to press the president to stop the caravan.

“The Mexican government is fully engaged in finding a solution that encourages safe, secure, and orderly migration,” State Department spokeswoman Heather Nauert told the Associated Press on Saturday, “and both the United States and Mexico continue to work with Central American governments to address the economic, security, and governance drivers of illegal immigration.”