Roy Ngerng Yi Ling, a 33-year-old healthcare worker, had posted an article on May 15 that was seen as accusing Lee of corruption.
But in a blog post Friday, Ngerng said the article had contained an allegation against Lee that was "false and completely without foundation".
"I unreservedly apologise to Mr Lee Hsien Loong for the distress and embarrassment caused to him by this allegation," wrote Ngerng.
Lee's lawyer Davinder Singh wrote to Ngerng on Sunday demanding an apology and compensation, saying the article implied that "Lee Hsien Loong, the Prime Minister of Singapore and the chairman of GIC, is guilty of criminal misappropriation of the monies paid by Singaporeans to the CPF (Central Provident Fund)".
GIC is a sovereign wealth fund that manages more than $100 billion of the city-state's foreign reserves. CPF is the state pension fund.
Ngerng has said he penned the article in an attempt to call for greater transparency on how the CPF is invested by the government through its two sovereign wealth firms.
He took down the article and links to it on his Facebook pages on Tuesday in compliance with the prime minister's demand.
But the blogger's lawyer M. Ravi dismissed the demand for compensation, while urging Lee not to seek damages.
"This would be so as to not reduce our client to a most assuredly disadvantaged position," Ravi wrote in a letter to Lee's lawyer on Friday.
He said Ngerng welcomed "an opportunity to have an open dialogue" with Lee regarding the CPF.
Singapore has ranked top in surveys as one of the world's least corrupt countries, but international human rights groups have regularly accused its leaders of using financially ruinous libel actions to silence critics and political opponents.
Singaporean leaders, including Lee and his father, former prime minister Lee Kuan Yew, have countered that the lawsuits are necessary to protect their reputations. (AFP)
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