WASHINGTON — Republican presidential candidate Herman Cain denied on Tuesday that he’s changing his story as he struggles to contain the fallout from sexual harassment allegations that could threaten his recently surging campaign. He also suggested his race could be a factor in the controversy.

The White House contender’s contradictory explanations over two days have raised questions about details of the allegations from back in the 1990s and about his current ability to manage a crisis in the national spotlight. The accusations, relating to his time as head of the National Restaurant Association, have surfaced just as he’s risen in national polls in the GOP nomination fight two months before the leadoff Iowa caucuses.

He said Tuesday night on Fox News that he believes there are some Democrats who want him defeated because he’s an unconventional candidate “achieving some unexpected, unconventional results,” and there could be some on the right “who do not want to see me because I am not the establishment candidate.”

Cain, who is black, said he believes race is also involved “but we don’t have any evidence to support it.”

A lawyer for one woman who complained about Cain’s behavior told The Washington Post on Tuesday she wants to talk publicly about it. According to that report, Joel P. Bennett, a Washington lawyer who specializes in employment cases, said he asked the National Restaurant Association to waive his client’s confidentiality so she can respond to Cain’s claims that the complaints were “totally baseless and totally false.”

Bennett did not immediately return messages seeking comment from The Associated Press.

In Sunday night’s original report by Politico, at least two women who had complained about Cain were said to have agreed to settlements that included stipulations that they not repeat their allegations in public.