Social Democrat TD Catherine Murphy has said the disposal of personal papers and disappearance of a SIM card belonging to the ex-Garda Commissioner Martin Callinan is one of the "key reasons" for the Dáil to be recalled.
Ms Murphy last night became the latest TD to express concern over the Fennelly report finding that potentially valuable information was not made available to the Commission.
And Renua leader Lucinda Creighton said she believed the disappearance of the items now warrants a garda investigation.
In his report, Mr Fennelly said it has been striking how little documentary evidence was available to his team.
Mr Callinan told the Commission that he had cleared out all personal papers after he announced his retirement, and he did not have any written notes to support his evidence, particularly in relation to informing Brian Purcell, Secretary General of the Department of Justice, about the issue of the telephone recordings.
He was able to produce his diary for the year 2014.
On March 25, Mr Callinan went to a filing unit in the Conference Room, where he kept personal papers, and requested black refuse sacks as he wished to sort through his files.
He later asked a Superintendent to dispose of eight to 10 bags of personal papers, which were shredded on April 4, 2014.
The report also details how the SIM card in Mr Callinan's phone was removed and subsequently destroyed.
The Commission again wrote to Mr Callinan and asked him to search for the phone.
He found it and furnished it to the Commission but it had no SIM card in it and no information stored on it.
Assistant Commissioner Jack Nolan stated that the SIM card had not been returned by the former Commissioner and had been cancelled remotely on May 30, 2014.
It subsequently emerged the contents of text messages were not retrievable.
The issue of the shredded papers and missing SIM are among the factors that prompted calls to recall the Dáil next week to discuss the report.
Renua leader Lucinda Creighton said she believed the revelation warrants a "garda investigation".
"The idea that we would just throw our hands in the air and say 'this is terrible' but do we don't pursue it is to my mind completely wrong," she told 'RTÉ's Today with Sean O'Rourke'.
Social Democrat TD Catherine Murphy expressed concern over the revelations and said she will press for the Dáil to be recalled.
"This is one of the key issues why we believe the Dail should be recalled to discuss these matters on the floor of the house," the Kildare North TD told the Irish Independent.