Speaking in Alaska, Secretary Mattis named the Texas bases but did not say whether they would house migrant children or families held together.
The Pentagon said last week it planned to house 20,000 detained children on military bases.
Meanwhile, Mr Trump repeated calls for deportations without judicial process.
…In his remarks, the defence secretary [defended the dramatic move as] a “legitimate governmental function.”
…The shelters will be run by HHS and not the Pentagon, according to the Associated Press, and facilities may be available as early as July.
US immigration officials say 2,342 children were separated from 2,206 parents from 5 May to 9 June.
While the adults are held in custody pending court appearances, the children are being sent to holding cells, converted warehouses and desert tents under the “zero tolerance” policy introduced in April.
Officials have gone to court to try to lengthen the time children can be held as parents are prosecuted.
…[Trump] has not made a distinction between economic migrants and those seeking asylum in his Twitter posts.