Up to 90 email accounts were compromised during the cyber-attack on Parliament on Friday.
Fewer than 1% of the 9,000 users of the IT system were impacted by the hacking, said a parliamentary spokesman.
The hack prompted officials to disable remote access to the emails of MPs, peers and their staff as a safeguard.
The spokesman said the attack was a result of "weak passwords" and an investigation is under way to determine whether any data has been lost.
Both Houses of Parliament will meet as planned on Monday and plans are being put in place to allow it to resume its wider IT services, said officials.
A number of MPs confirmed to the BBC they were unable to access their parliamentary email accounts outside of the Westminster estate following the hacking.
