"No, there's nothing to shoot down," Cain said, citing the restaurant association's policy of not discussing personnel matters with the press.
Cain also said that the campaign was not faster to deny the allegations because they had been anonymously sourced and he did not want to give credence to the reports.
"We're not going to chase anonymous sources when there's no basis for the accusation," Cain said.
But Cain Chief of Staff Mark Block confirmed that Politico, which originally reported the story, had provided the campaign information about the accuser.
"I think they did pass a name on, correct," Block said.
Still, the candidate seemed eager to put the issue to rest, saying he would be "delighted to clear the air."
"Enough said about the issue, there's nothing else there to dig up," Cain said.
Cain, at one point during his National Press Club remarks, used a napkin to wipe his brow but he answered all the questions about the event forcefully and played to the crowd, trying to illicit laughs.
"As a result of today's news story, I really know what it feels like to be No. 1," he joked.
The room was packed for his remarks and Cain joked, "This many white people can't pretend that they like me."
He ended his time at the press club by breaking into song, singing "Amazing Grace."