Sinn Féin leader Gerry Adams, Social Democrats co-founder Catherine Murphy, and Independent TD Mick Wallace all said a detailed examination of the new allegations is now needed.
BBC’s Spotlight programme on Monday broadcast secretly recorded conversations involving former Nama adviser Frank Cushnahan, who was central to the sale of the agency’s Project Eagle portfolio.
The deal has been the subject of intense scrutiny for more than a year because over stg£4.3bn worth of assets was bought by US vulture fund Cerberus for stg£1.3bn in 2014.
The BBC investigation detailed secret conversations at a Belfast hotel in which Mr Cushnahan admitted he was in line to receive €7.7m from parties trying to buy the assets. He was meant to be giving independent advice on the assets.
The recordings claim he was in line for different payments at different times from would-be purchasers and some developers due to benefit from the sale, including Cerberus and rival bidder Pimco.
It is alleged that Mr Cushnahan was in line to receive €7.7m placed by the managing partner of law firm Tughans, Ian Coulter, in an Isle of Man bank account in late 2014.
This money has never been claimed.
Speaking to the Irish Examiner last night, Mick Wallace and Catherine Murphy both said a full independent inquiry is now warranted. This call was echoed by Gerry Adams.
The Department of Finance said all relevant information has already been released, and that Nama itself has done nothing wrong.
Nama said that it dealt with the claims thoroughly last year.