Bunning, R-Ky., made the comments Feb. 21, 2009, during a private fundraiser at which he mentioned the Justice's pancreatic cancer as "bad cancer -- the kind that you don't get better from," ABC News reported Wednesday.
Bunning later issued a statement misspelling the justice's name.
"I apologize if my comments offended Justice Ginsberg," Bunning said.
"I am pleased to report that, contrary to Sen. Bunning's prediction, I am alive and in good health," Ginsburg, 77, told an audience last week.
Ginsburg recently posted on the Supreme Court's Web site, saying she was "unsettled, indeed alarmed" by allegations by novice government employee Liz Cheney, who questioned the loyalty of U.S. lawyers representing former detainees at Guantanamo Bay charged with terrorist activities, ABC said.
"One of the nine was a former law clerk of mine, a young man of great intelligence, integrity and devotion to the ideals that make the U.S.A. a great nation," Ginsburg said.
Ginsburg praised lawyers who take unpopular clients on a pro bono basis.
"To that expression of the true America Way, one can only say Amen," she said.