Hackers are said to have been trying to access "soft" passwords
Senior MPs have said they still cannot access their emails today.
A House of Commons spokeswoman said: "The Houses of Parliament have discovered unauthorised attempts to access parliamentary user accounts.
"We are continuing to investigate this incident and take further measures to secure the computer network, liaising with the National Cyber Security Centre.
"We have systems in place to protect member and staff accounts and are taking the necessary steps to protect our systems."
"The lack of remote access to emails was not part of the attack but was due to measures taken by those trying to deal with the incident.
"Parliament has disabled remote access to protect the network," she said.
A spokesman for the National Cyber Security Centre said: "The NCSC is aware of incident and working around the clock with the UK Parliamentary digital security team to understand what has happened and advise on the necessary mitigating actions."