George Reid, the parliament's presiding officer, reiterated that the £431m total was correct in his report on the scheme in April.
He is due to publish his latest monthly report either next week or in the first week of June.
A parliament spokesperson said the building was due to be completed later this summer and will open in September.
The formal opening of the scheme by the Queen will take place on 9 October. It will cost £210,000.
The latest cost prediction comes as further details about the bad management of the scheme was revealed to the Fraser inquiry.
A written submission to the inquiry by David Ferguson, the audit adviser for the parliament, put the number of design changes made during the scheme at about 10,000.
He said: "Whatever the number of design changes, they have generated an additional cost of some £26m, according to my calculations."
Ferguson said that the practice of letting out packages of work with incomplete design information was "the least cost-effective way to manage the project".