Herman Cain On Sharon Bialek: 'I Don't Even Know Who This Lady Is'

Republican presidential candidate Herman Cain categorically rejected on Tuesday that he remembered Sharon Bialek, who came forward Monday with high-profile attorney Gloria Allred and accused Cain of groping her in the 1990s.

"I reject all of these charges," he said in a Tuesday interview with ABC News' Jonathan Karl. "I don't remember this person by name, I don't remember that she worked at the education foundation. I didn't even recognize her." He added later, "I don't even know who this lady is."

When asked whether Bialek was lying, he said, "Yes. I am saying that in as nice a way as I can."

Bialek alleges that Cain behaved inappropriately toward to her in 1997 when she was looking for a job after being let go from the National Restaurant Association Education Foundation.

"Instead of going into the offices, he suddenly reached over and put his hand on my leg, up my skirt, and towards my genitals," she said. She recalled that when she protested the advances, Cain said, "You want a job, right?"

Cain rejected that he would leave the race because of the allegations. "I am not going to let these accusations, which are baseless, bogus and false stop me," he said. "I'm not discouraged to the point that I'm going to pull out because of these attacks."

He said his wife, Gloria Cain, who has not done any interviews and canceled one on Fox News last week, was supportive of him. "Today, she is 200 percent supportive of me." The former Godfather's Pizza CEO described her response: "She said, 'I've known you for over forty years, that doesn't even sound like you.'" He said she would do interviews "when it's the right time and when she's ready."

He said former Massachusetts Gov. Mitt Romney was right when he said earlier on Tuesday that the allegations were "particularly disturbing." "Well he's right, they're disturbing to me; they're serious," Cain said. "My response is there's absolutely no basis to them."

The interview touched on other subjects as well. He said he would favor a constitutional amendment prohibiting children of undocumented immigrants from becoming citizens. He then contradicted that statement, adding, "I do not support tampering with the fourteenth amendment," which says that anyone born on United States soil is a citizen.