Matthew Craig Barrett was arrested on Saturday morning, hours after his arrival in Islamabad, Dawn online quoted the ministry as saying.
The ministry has ordered an investigation into the grant of a Pakistani visa to Barrett, who was expelled from the country after being caught spying on sensitive installations.
Barrett was on Saturday arrested by the Federal Investigation Agency in a raid on a guest house in Islamabad.
Interior Minister Nisar Ali Khan has suspended an FIA official as well as immigration staff on duty when Barrett was cleared by authorities at the airport.
A statement by the ministry said action would be taken against the officials at the Pakis-tani consulate in Houston for issuing a visa to Barrett.
According to a document cited by Dawn, Barrett was issued a multiple-entry visa, stamped by an official from Pakistan's mission in Houston.
The visa was issued on June 22 and was valid up to June 30, 2020, allowing Barrett to stay in the country for up to one year at a time.
Barrett was arrested and deported from Pakistan in 2011 for overstaying his visa.
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