Goh's lawyer (L) caught up with Chee at an election rally
The threats from former prime minister and now elder statesman Lee Kuan Yew, and Prime Minister Goh Chok Tong, concern remarks by Mr Chee that the government had lent $10bn of public money to former Indonesian President Suharto during the 1997-98 Asian economic crisis.
The Singapore Government says the loan never went ahead.
But Mr Lee refused to rule out continuing legal action, saying the amount of damages offered by Mr Chee could determine his next step.
Mr Goh earlier said a lawsuit may be necessary to maintain his reputation at home and overseas.
Awkward encounter
The episode began on Sunday when Mr Chee encountered Mr Goh while campaigning for the 3 November election in a suburban neighbourhood. Mr Chee challenged his opponent to answer questions regarding the alleged misuse of public money.
Mr Chee later said he wanted to ask Mr Lee the same questions.
When both Mr Lee and Mr Goh threatened potentially ruinous legal action unless he apologised and paid damages, Mr Chee offered an apology but was rejected as being insincere and inadequate.
Now, he will have to wait to see if his latest offering is judged sufficiently contrite.
Free-speech issue
Critics of the government say opposition is often stifled through defamation cases in which damages can run into hundreds of thousands of dollars.
They say it is a method of imposing tight restrictions on free speech and the media.
But government officials say it is legitimate to protect reputations from unfair attack.
The row has stimulated public interest in what had become a non-election after the opposition guaranteed a victory for the ruling People's Action Party (Pap) by contesting fewer than half the seats available.
The Pap has governed Singapore since independence in 1965, with opposition parties never gaining more than four seats.
Singapore's opposition is fragmented into 22 parties. They won just two seats at the last election in 1997 when they also contested fewer than half the seats. The Pap last faced a full election in 1988.