The cross-party committee, which has an SNP majority, said the case had not been made for the change and it recommended the Scottish Government considers removing the provisions from the Criminal Justice (Scotland) Bill.
MSPs on the Justice Committee said they were "concerned that the case for abolition has paid insufficient regard to the importance of this requirement within the Scottish criminal justice system".
There were suggestions last night that absent members and substitutes may have affected the outcome.
As they published their report, the Scottish Government announced former High Court judge Lord Bonomy is to head up a special group, looking at what safeguards might be required if corroboration is abolished.
Mr MacAskill said he remained "committed to this essential and long-overdue reform as the corroboration rule can prevent strong cases which could be prosecuted in other jurisdictions from being taken forward".
He added: "Scotland is the only country in the world which has been identified as having the requirement and this is acting as a barrier to justice."
But MSPs on the Justice Committee said: "The majority of committee members are of the view that the case has not been made for abolishing the general requirement for corroboration and recommend that the Scottish Government consider removing the provisions from the Bill."
Convener Christine Grahame said the Scottish Government needed to provide "much more information on its plans to review additional safeguards" before the Scottish Parliament votes on the general principles of the Bill.
Tory justice spokeswoman Margaret Mitchell called the report "damning" and added: "If Kenny MacAskill has any respect for the Scottish Parliament he must now take corroboration out of the Criminal Justice Bill so that it can be properly considered."
The committee has been scrutinising the Scottish Government's Criminal Justice (Scotland) Bill, which includes plans to abolish the centuries-old requirement for corroboration, meaning that evidence against an accused person must come from more than one source.
Senior judge Lord Carloway called for the change in a review of the criminal justice system, insisting corroboration was "an archaic rule that has no place in a modern legal system".
The proposal was welcomed by the police and victims' groups. But there has been fierce opposition in the legal profession.
The committee was "not convinced" ending the requirement would improve justice.