WASHINGTON — The Pentagon said on Wednesday that it would build temporary housing along the southwestern border for 7,500 migrant adults facing deportation, the latest step in the administration’s efforts to respond to a surge of undocumented immigrants and asylum seekers trying to enter the United States.

The Defense Department will loan military-style tents to the Department of Homeland Security, Pentagon officials said. In a statement emailed to reporters, Maj. Chris Miller, a Pentagon spokesman, said that military personnel would only set up the tents and that the operation of the facilities would rest with homeland security.

The cost for putting up the tents — to be constructed near Tucson, as well as near Tornillo, Donna, Laredo and Del Rio, Tex. — will be determined after the Pentagon conducts on-site assessments over the next two weeks.

Detention centers at the border have been pushed to overcapacity as an increase of migrants, most of them from Central America, have crossed into the United States. Officials recently said they would spend millions on the construction of tent cities in Texas, and they also began flying migrants to facilities with more space in Del Rio, Tex., and in California.