Nicola Sturgeon has said the situation involving former MP Michelle Thomson was "not easy" for the SNP.
The former Edinburgh West MP resigned the party whip and was eventually deselected amid fraud allegations against a former business associate.
However, she said she was given no choice in the matter and asked for an apology from party leader Ms Sturgeon.
Ms Sturgeon said she appreciated the ex-MP "has had a really tough time", but said it "wasn't easy" for the SNP.
The first minister said it was for the party to discuss Ms Thomson's "future relationship" with the SNP going forward.
Ms Thomson was elected SNP MP for Edinburgh West in the 2015 general election, taking the seat from the Liberal Democrats and immediately being installed as the party's business spokeswoman. However, she resigned the party whip in September that year following allegations about past property dealings.
She was one of five people named in a report sent to prosecutors by Police Scotland more than a year later, but the Crown Office ultimately concluded that there should be "no criminal proceedings at this time" due to an "absence of sufficient credible and reliable evidence".
Ms Thomson always strongly denied any wrongdoing, insisting all deals her business took part in were both legal and fair, but was deselected by the SNP ahead of June's snap general election. The seat was subsequently re-taken by the Lib Dems.
Ms Thomson said she thought Ms Sturgeon may have "panicked" at the time the allegations were first made, as she was "relatively new in her role".
She said she was given "no support" and had "no chance to put across my side of the story", saying she was given no option but to resign the party whip at Westminster.
Deputy First Minister John Swinney has insisted that "the decision to withdraw from the party whip was Michelle's decision", adding that it was "taken as a consequence of conversations with those responsible for conduct matters within the party".
Ms Thomson was also critical of the media's "absolutely unfair" portrayal of the affair, calling for an apology from the BBC for its coverage.
Asked about Ms Thomson's account, Ms Sturgeon said "clearly on some aspects I would take a different view", but said she did not want to go into detail.
She said: "I regret very much that we were confronted with a situation where one of our newly-elected MPs was facing serious allegations - of course I regret that.
"It wasn't a situation of my making, it wasn't a situation clearly I would have chosen to be in. And I appreciate that what followed on that, the investigation that took place, was not easy for Michelle Thomson and it wouldn't have been easy for anyone in that situation.
"But I think people would also appreciate that it wasn't a particularly easy situation for the party to be in either.
"Michelle is now, happily, in the position where she can put this behind her. She has been cleared of any wrongdoing and I am sure she is very relieved about that so we can now look forward and have a discussion directly with her.
"But with the greatest of respect we will have the discussion, if she wants to have it, with her and not through the medium of the BBC."