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Department of Homeland Security Secretary Kristjen Nielsen tweeted that DHS would continue "to support our Mexican partners as they take steps to confront the crisis on their southern border. The Mexican federal police are handling this in a professional and humane manner."
She added in a subsequent tweet that she has been in “constant contact” with her foreign counterparts in Mexico, Guatemala and Honduras, and that her department was monitoring the situation and ready to provide assistance if necessary.
I have been in constant contact with my foreign counterparts in Mexico, Guatemala and Honduras. Closely monitoring developments and providing any requested assistance.— Sec. Kirstjen Nielsen (@SecNielsen) October 20, 2018
Thousands of migrants reached the Guatemala-Mexico border on Friday, breaking through a fence on the Guatemala side of a bridge separating the two countries. On the Mexican side of the bridge, they were met by Mexican police in riot gear. Others, meanwhile, waded into the Suchiate River or took rafts to get to Mexico.
Many of the migrants are seeking refugee status in either Mexico or the United States.
The Mexican Interior Ministry said on Saturday that 640 Honduran migrants have requested refuge in Mexico. It also said that priority attention would be given "164 women, some of them in advanced stage of pregnancy; 104 girls, boys and teenagers, who are from 3 months old to 17 years old; as well as older adults who have varying degrees of disability. This group includes a minor who traveled alone."
President Trump threatened in a series of tweets on Thursday to “call up the U.S. military and close our SOUTHERN BORDER” if Mexico doesn’t do anything to stop the flow of migrants moving north.
I am watching the Democrat Party led (because they want Open Borders and existing weak laws) assault on our country by Guatemala, Honduras and El Salvador, whose leaders are doing little to stop this large flow of people, INCLUDING MANY CRIMINALS, from entering Mexico to U.S.....— Donald J. Trump (@realDonaldTrump) October 18, 2018
....In addition to stopping all payments to these countries, which seem to have almost no control over their population, 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!..— Donald J. Trump (@realDonaldTrump) October 18, 2018
The president also blamed Democrats at a rally on Friday night in Arizona for the illegal border crossings.
Yet, it seems that Mexico will continue to process migrants. The Interior Ministry said in its statement that migrants will begin the refugee application process at the country’s National Institute of Migration, where their data will be collected, before they are sent to shelters that have been “enabled for their accommodation.”
The Mexican government also released handout video of migrants on a bus being told by an official that they would be assisted in being processed for any asylum claims they may have.
ABC News' Amanda Maile and Joshua Hoyos contributed to this report.