Trump made similar threats to shut down the southern border late last year, but ultimately ended up not following through on the threats.
The president's threat sets up his first confrontation with Mexico's new president, Andrés Manuel López Obrador, and comes as U.S. Customs and Border Protection (CBP) has reported that it has reached capacity for housing migrants at facilities in both Texas and Arizona.
The overflow has resulted in Border Patrol agents releasing migrant families in groups of hundreds at a time in Yuma, Arizona, as well as El Paso, Texas, according to the agency.
In his tweets Friday, the president accused Mexico of avoiding taking action to stop illegal border crossings.
"This would be so easy for Mexico to do, but they just take our money and 'talk,'" the president charged. "Besides, we lose so much money with them, especially when you add in drug trafficking etc.), [sic] that the Border closing would be a good thing!"
CBP Commissioner Kevin McAleenan said a day earlier that illegal border crossings had reached a "breaking point" for his agency.
“For the first time in over a decade, CBP is performing direct releases of migrants when [Immigration and Customs Enforcement] is unable to provide bed space to relieve overcrowding,” McAleenan said.
"We are doing everything we can to simply avoid a tragedy in a CBP facility,” he added. “But with these numbers, with the types of illnesses we’re seeing at the border, I fear that it’s just a matter of time.”
The news also comes just days after the president nominated a Washington-based attorney, Christopher Landau, to be the next U.S. ambassador to Mexico.