WASHINGTON — The scandal engulfing US Republican presidential hopeful Herman Cain deepened Thursday as one of two women accusing him of sexual harassment issued a statement on the allegations.

Cain, who has had a meteoric rise in the polls to join former Massachusetts governor Mitt Romney at the head of the Republican field, insists he is innocent of harassing two women when he was president of the National Restaurant Association between 1996 and 1999.

Joel Bennett, a lawyer for one of the unknown women, lodged a written statement with the association that could for the first time tell her version of the story and reveal the exact nature of the allegations.

The association said its lawyers would decide Friday whether the confidentiality clause in the financial settlement it brokered with her back in the 1990s could be lifted and her statement made public.

"Our outside counsel was contacted by Mr Bennett today and was asked to provide a response to a proposed statement by tomorrow afternoon," said the association's senior vice president for public affairs, Sue Hensley.

"We are currently reviewing the document, and we plan to respond tomorrow."

Bennett had previously indicated that his client was angry at Cain's response and keen to set the record straight.

"Naturally, she's been very upset about all of this since the story broke last Sunday because Mr Cain has been giving the impression that she's someone who came out and made false allegations and that?s certainly not true," he told CNN.

News website Politico, which broke the story on Sunday night, said it had learned that the woman received a $45,000 settlement.

The New York Times had already reported that a second association employee accusing Cain of sexual harassment received $35,000, a year's pay.

After initial denials, Cain belatedly conceded on Tuesday that he was aware that a female employee of the association had received a paid settlement but continued to deny any knowledge of the second alleged case.

His stumbling response, which has included several contradictions, has raised doubts about the political outsider's ability to campaign under the harsh glare of the media spotlight.

The Cain campaign has boasted that it is raking in more campaign contributions than ever despite the scandal.

Political experts doubt the former CEO of the Godfather's Pizza chain, who has never before held elected office, will maintain his surprise run in the polls to win the Republican nomination and challenge Obama in November 2012.

How he emerges from the sexual harassment scandal is likely to determine whether he is a serious contender when the Republican primaries, the state-by-state battle for the nomination, begin in earnest in January.