Labour's state-owned enterprises spokesman Clayton Cosgrove said it was a serious matter that Solid Energy had declined Dr Elder's earlier offer to appear before the committee.
He said that directly contradicted the response of Solid Energy's acting chief executive Garry Diack, who told the committee he was not aware that Dr Elder had approached anybody about appearing.
"So we have a very serious issue which leads to a greater call for inquiry, and that is I think certain individuals may be in danger of misleading Parliament," he told Radio New Zealand this morning.
"If people can't get their stories straight about who was available, who was turned down, who made themselves available, this creates further murk about this whole issue."
Mr Cosgrove said Mr Diack would have to be called back before the committee.
He said Dr Elder's appearance would be a good start, but a full inquiry was needed into why $389m went "down the toilet".
"It goes beyond Dr Elder now and there's enough murk around this, there's no excuse now for not having a full parliamentary inquiry.
Deputy Prime Minister Bill English told TV3's Firstline this morning it was up to Solid Energy whether Mr Elder appeared before the committee.
"But whatever is said there is going to be about history that we can't change. Our focus at the moment is very strongly on seeing what we can do to get this company into some kind of viable state to ensure that it can contribute to the economy and that people have got jobs."
Mr English said he would be interested in hearing what Dr Elder had to say.
"But it's not going to effect the negotiations and decisions that have to go on now about how Treasury work with the company and the banks to get to some kind of viable operation."
Mr English said what happened at Solid Energy was not inevitable, and there were some hard lessons to be learned.
Asked why the Government had not put more pressure on Dr Elder to appear, Mr English said that was a matter for the committee.
Dr Elder said last night that he had "always been willing to answer any question members of the committee may have about Solid Energy and my time as its chief executive".
"I made myself available to assist the Solid Energy team at last week's sitting of the committee, but was advised that I was not required to be present,'' he said in a statement.
"I have never refused to cooperate. I will endeavour to help the committee in any way I can, subject to the lifting of obligations imposed on me by Solid Energy."
A spokeswoman for Solid Energy said reports that Dr Elder was still receiving a $1.3m salary were incorrect. She said Dr Elder's $850,000 base salary before performance-based incentives was more likely to reflect his current pay rate.
Read more: Elder agrees to face grilling
- With APNZ