The US Treasury Department in a statement said the Ministry of Intelligence and Security directs several networks of cyber threat actors, including those involved in cyber espionage and ransomware attacks in support of the Iranian government.
The ministry was already designated under US sanctions. Iran's mission to the United Nations in New York did not immediately respond to a request for comment.
Microsoft, whose cybersecurity research team investigated the incident, said in a blog post on Thursday that the Iranian cyber operation involved a combination of digital espionage techniques, data wiping malware and online information operations.
The goal of the hackers, according to researchers, appeared to be to embarrass Albanian government officials.
The July attacks temporarily disrupted government websites and other public services. Analysts say the operation was intended to punish Albania for supporting an Iranian dissident group based in the country, known as the Mujahedin-e Khalq (MEK).