Tories and Lib Dems united to demand the controversial part is ripped out of the Criminal Justice Bill, currently going through the Scottish Parliament.
The centuries-old rule means evidence must come from at least one source. Critics say it can deny justice to people, particularly in rape cases, but there are concerns that the change is being made too quickly and without necessary safeguards.
In light of those concerns, Mr MacAskill said former high court judge Lord Bonomy will lead a special group looking at what might be needed to prevent miscarriages of justice. But he is also committed to keeping the intention to scrap the rule within the Bill.
His announcement came as Holyrood's Justice Committee said the case has not been made to ditch corroboration.
Tory leader Ruth Davidson highlighted the report during First Minister's Questions.
"This is now about the integrity of this Parliament," she said.
"What we as members are being asked to do is to vote through a Bill which we know to be deeply flawed on the grounds that Kenny MacAskill says he'll sort it later.
"There is an obvious solution here. Leave the scrapping of corroboration out of the Bill. Ask Lord Bonomy to report on the whole issue and then let us look at it again.
"Surely it is better to make good law later than bad law now."
Lib Dem leader Willie Rennie supported Miss Davidson, adding that the Scottish Government's approach is "crackers".
He said: "Appointing Lord Bonomy doesn't restore justice, it simply papers over the cracks with a veneer of respectability.
"Isn't it better to work out the fix before you deliberately cause the problem? Law making in reverse is a shoddy way to expect Scotland's Parliament to act."
But Mr Salmond said the attack is unfair.
"It's not a quick fix, it's a distinguished judge who's looking to make absolutely certain that as this change is made, appropriate safeguards are there to prevent miscarriages of justice," he said.
"That is a substantial point and any recommendations before implementation would have to come back to the committee, back for discussion, and back to this Parliament for approval.
"By definition, this change cannot take place unless and until this Parliament is satisfied with the proposals that come forward."
There is a "real problem" with corroboration, he added.