"I hope you would agree with me that this is the democratic right of our citizens to be well informed about their choices. There is no better opportunity for candidates to weigh candidates' abilities, character and vision," Premadasa said in the letter, copies of which were released to the media on Sunday.
"Indeed, the way candidates respond to their opponents on their feet is often seen as an indication of how they would govern under adversity or respond in a crisis.
"On Wednesday (October 30), I invited you to take up the challenge of facing the nation at such a debate. Unfortunately, I am yet to receive a response. Some of your advisers have alluded to the absence of a formal written invitation, even in this age of technology and digital communication," he added in the letter.
Premadasa asked Rajapaksa to take the challenge of facing the nation together and putting their respective policies and vision to the test on a public stage, reports the Daily Financial Times.
"Let us show the public that we value the democratic tradition of spirited debate and that we encourage voters to asses us critically. Let us show them we have nothing to hide and we are not afraid," Premadasa said.
Premadasa concluded by saying that he hoped there would be a response to his formal written invitation.
A record 35 candidates have filed their nominations for the island nation's eighth presidential election, with incumbent President Maithripala Sirisena's term coming to an end in January 2020.
Rajapaksa and Premadasa have already emerged as the two favourites in the fray.
Gotabaya, who served as the Defence Minister in his brother Mahinda Rajapaksa's administration, oversaw the end of Sri Lanka's brutal 25-year civil war in 2009.
Sajith is the son of late President Ranasinghe Premadasa, who ruled the country with an iron fist before he was assassinated by a Tamil suicide bomber on May 1, 1993.
( With inputs from IANS )