Peter Murrell, who is married to the SNP leader and First Minister Nicola Sturgeon, appeared in front of the inquiry on Tuesday.
However, he looks set to be called to give evidence again after what was described as a “squirming performance” involving “half-truths and untruths”.
It is understood he may appear ahead of Ms Sturgeon who is likely to be called to give her evidence in the new year and the decision follows calls from opposition members of the committee unhappy at the credibility and quality of his evidence.
Particular attention will be taken of Mr Murrell’s denial of his use of the messaging app WhatsApp which the Scottish Sun reported was inconsistent with an account found under his mobile number which was used as recently as November.
The Scottish Conservative’s Murdo Fraser, who sits on the committee, labelled Mr Murrell’s evidence session “shambolic” and “sleekit”.
He said: “In a shambolic evidence session, Peter Murrell managed to contradict not only Nicola Sturgeon but himself, all in the space of a few hours.
“His answers were sleekit from start to finish. One minute he was in the house for a crunch showdown with Alex Salmond, then he wasn’t. He knew about the meeting beforehand, then he didn’t.
“He told the committee he is one of the few people not to have WhatsApp – only for it to emerge he used it a few weeks ago.
“He tied himself in knots answering the simplest of questions and spoke in riddles.
“The SNP chief executive must return to the committee to clear up the contradictions in his evidence and this time, provide entirely truthful answers.”
Scottish Labour deputy leader and committee member Jackie Baillie said: “Peter Murrell must explain the contradictions and discrepancies in his evidence to the Committee yesterday as a matter of urgency.
“Mr Murrell’s squirming performance has cast doubt over the First Minister’s account of what happened, and poses a serious question over whether Nicola Sturgeon breached the Ministerial Code by having a clandestine meeting with Alex Salmond.
“I know it’s the pantomime season, but it is time for Mr Murrell to tell the truth, the whole truth, and nothing but the truth to the committee.”
Alex Cole-Hamilton, the Scottish Liberal Democrat member of the committee said it would be “dead wrong” of Mr Murrell to assume the committee was convinced by his appearance.
He said: “If Peter Murrell thinks that half-truths and untruths will convince the committee to give up its enquiries, he is dead wrong.
“The public are not being well served by sneakiness and evasion. With significant doubts now cast over the evidence he gave, Peter Murrell should return to the committee for further questioning.
“If this is the level of co-operation the public can expect from the Sturgeon-Murrell household, then we are in for a long and painful process.”
He added: “This is because revelations in today’s papers, particularly around his use of WhatsApp, undermine the credibility of the evidence we heard yesterday.”