"At the moment, we know three Japanese nationals are dead and three injured," Abe told reporters.
"No matter what the reasons were, terrorism can never be forgiven. We strongly condemn this," he said, adding that Tokyo was still working to collect information.
"We will exert the utmost effort in our fight against terrorism by deepening cooperation with the international community."
Chief Cabinet Secretary Yoshihide Suga denied that Japan's death toll from the attack, announced by Tunisian Prime Minister Habib Essid, had hit five.
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Among the wounded Japanese was Noriko Yuki, 35, who was visiting the museum with her mother.
"I was crouching down with my arms over my head, but I was shot in the ear, hand and neck," she said from her hospital bed, in footage broadcast by NHK.
"My mother beside me was shot in the neck. Mother couldn't move by herself when the police came over..."
In the footage, Yuki did not say exactly what had happened to her 68-year-old mother, only that she was rushed to a separate hospital for surgery.
The brazen daylight raid sparked panic at the nearby parliament and the National Bardo Museum itself, a magnet for the tourists who contribute so much to the economy.
There were conflicting reports from various governments about the precise death toll for each country, although Tunisia said there were also fatalities from Italy, Colombia, Australia, France, Poland and Spain.
It was the second time Japan has become embroiled in Middle East violence this year after the execution-style murders of a journalist and his friend by Islamist extremists in January.