The Mexican Ministry of Foreign Affairs noted it would authorise temporary entry for certain foreigners from the United States "due to humanitarian reasons", adding, however, that the country had every right to refuse entry of the foreigners into the country.
The statement comes after Washington warned that the US might send non-Mexican migrants who breached the border back to Mexico.
"Effective immediately individuals arriving in or entering the United States from Mexico — illegally or without proper documentation — may be returned to Mexico for the duration of their immigration proceedings", Homeland Security Secretary Kirstjen Nielsen said
READ MORE: 'We Will Win on the Wall' Against the Democrats — Trump
Earlier in the day, US president Donald Trump reiterated his support for the border wall project, stressing that Congress has to pass funding bills for several government agencies, including the DHS, in order to avoid a partial shutdown of the federal government.