Nouri al-Malik is facing a surge of protests by Iraq's Sunni minority, tensions with the autonomous Kurdish region and discontent among fellow Shiites.
A statement on his website Saturday compared him to Bashar Assad, the Syrian leader who brutally cracked down on an uprising against him that has turned into a civil war.
The statement by "Team Kuwait Hackers" told the Iraqi leader, "You want to be like Bashar Assad ... Bashar is over."
The message was accompanied by a picture of wailing black-clad women in mourning. It was up for several hours until the site was taken down.
Telephone calls to al-Maliki's office went unanswered.