Blogger Roy Ngerng said on Saturday that he "has no answer" as to whether he will make an offer of damages and legal costs by Monday, after Prime Minister Lee Hsien Loong refused his request to drop them.
In a 14 minute video Mr Ngerng recorded and put on his blog The Heart Truths, he also said he does not regret what he has done.
"On Monday the Prime Minister wants me to reply to him how much damages and costs I'm willing to pay to him," he said in the video.
"I do not have an answer. I'm only an ordinary Singaporean, I'm not the Prime Minister. I just want to question what is right. I just want to question what is going on for Singaporeans and I want to speak up on behalf of Singaporeans. As I have shown you, it is clear that some things are missing in how the CPF is reported."
Mr Ngerng again criticises how the CPF is managed in the video, and adds: "I will continue to do what I can for as long as I can. But with this law suit you can be sure that I may not be able to do further."
PM Lee took issue with a blog post on May 15 in which Mr Ngerng alleged that he had misappropriated CPF funds.
In a letter of demand sent by Mr Lee's lawyer Senior Counsel Davinder Singh on Sunday, Mr Ngerng was asked to take down the post, apologise publicly and pay damages and legal costs or face legal action.
Mr Ngerng took down the post the next day. Then on Friday, he apologised "unreservedly" to PM Lee on his blog, acknowledging that the claims he made were false and completely without foundation.
But in a letter sent to PM Lee's lawyer Mr Singh, he also pleaded not to have to pay damages and legal costs, and asked for a chance to have an open dialogue with the Prime Minister on the CPF.
The request to drop damages, however, was rejected and he is given until Monday 5pm to make an offer, otherwise legal proceedings will be started against him.
Mr Singh said in the letter that the damages "should reflect, among other things, the gravity of the false and malicious charge, the fact that your client knows and accepts that it is completely without foundation, its widespread circulation and the standing of our client".
Mr Singh added that the Prime Minister "reserves the right" to deal with other issues in Mr Ngerng's letter "at an appropriate time".