Stephen Flynn has denied that he told Ian Blackford weeks ago that the SNP Westminster group had a new auditor in place.
Blackford said that he had been told by Flynn, who succeeded him as SNP Westminster leader, in a phone call on April 7 that the group had a new auditor in place.
But Flynn said that "there is difference between stating that you are likely to secure an audit firm and having one."
He added that "working to secure an audit firm" does not "equate to having an audit firm in place".
The Westminster group has not had auditors in place since September.
Blackford accused Flynn of giving him false assurances about the auditors. He told the BBC that Flynn had contacted him on April 7 to say that a new auditor was being appointed.
He later shared the story on Twitter and said: "Let me be quite categoric that I was phoned on the 7th April by Stephen [Flynn] and told this information."
But during a question and answer session at the Institute for Government think tank in London on Tuesday afternoon, Flynn denied Blackford's version of events.
He said: "I think it's important to reflect that when we are talking about this, obviously there's a lot of staff involved. I don't want to speculate in too much detail in relation to that until they have certainty.
"Is it the case that we've been working to secure an audit firm? Absolutely it's the case. Am I hopeful that we'll be able to do that? Absolutely.
"Does that equate to having an audit firm in place? Does that equate to having certainty that I will be able to meet the deadlines which have been placed upon us by the House of Commons? No.
"I'm not going to provide a categorical assurance and solution to that. Those that have provided categorical assurances in relation to that, would probably have been wise not to have done so."
When asked if Blackford was lying, Flynn said: "The difference, if I may, between stating that we are likely to secure an audit firm and having an audit firm.
"There's also a big difference between seeking to secure an audit firm and being able to provide certainty that you will meet deadlines.
"I have not sought to, in any way, suggest that we would definitely meet any of our deadlines and obligations because I don't think that was the right tact to take.
"Indeed, the process to secure an auditor is still very much underway as it was when myself and Ian [Blackford] spoke."
Flynn had said on Monday that the party could lose out on more than £1million in public funding and be forced to cut staff if the Westminster group does not find auditors by the end of next month.
Flynn also said that he had asked the authorities for an extension from the May 31 deadline but that they had not yet gained one.
He said: "We did ask the House of Commons authorities in respect of that. It's my understanding that the 31st of May is the deadline and that's what needs to be kept."
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