Remote access was still restricted "as a precaution" the group said.
Oil production was not affected by the virus which struck on 15 August, Saudi Aramco added.
The company took its website offline after the attack and now carries a message on its front page apologising for any inconvenience.
"We have isolated all our electronic systems from outside access as an early precautionary measure that was taken following a sudden disruption which affected some sectors of our network," the message reads.
Most of the damage has now been repaired, it added.
A group named the Cutting Sword of Justice has claimed responsibility for the attack in an online forum.
It blamed the Saudi government for "crimes and atrocities" in several countries. It said the state-run oil firm was hit because it was a key source of income for the government.
"This was not the first nor will it be the last illegal attempt to intrude into our systems," said Khalid al-Falih, president and chief executive of Saudi Aramco.
Last week a virus called Shamoon, which targeted companies in the energy industry, was reported by security experts. Saudi Aramco has not said whether this was the malware involved.
About 30,000 workstation computers are back online at Saudi Aramco after a virus hit the world's largest oil producer.