A woman who said Herschel Walker paid for her abortion in 2009 is the mother of one of his children, according to a new report, undercutting the Georgia Republican Senate candidate’s claim to not know who she was.

The Daily Beast, which first reported the abortion, said it had agreed not to reveal details of the woman’s identity.

Walker, who has expressed support for a national abortion ban without exceptions, called the allegation a “flat-out lie”, threatened a lawsuit against the outlet and said he had no idea who the woman might be.

In a Thursday interview with the conservative radio host Hugh Hewitt, Walker repeatedly called the accusation “untrue”.

But Walker added: “If that had happened, I would have said there’s nothing to be ashamed of there. People have done that – but I know nothing about it.”

On Wednesday night, the Beast revealed that the woman was so well known to Walker that, according to her, they conceived another child years after the abortion. She decided to continue with the pregnancy, though she noted that Walker, as during the earlier pregnancy, expressed that it wasn’t a convenient time for him, the outlet reported.

The Beast said the Walker campaign declined to comment. Walker is scheduled to make a public appearance on Thursday morning in Wadley, Georgia.

The latest reporting ensures that abortion will continue to be a central issue in the Georgia race, one of the most competitive Senate contests. Walker and the Democratic senator, Raphael Warnock, are locked in a tight contest that is key to the balance of power in the Senate.

A series of stories have shaken Walker’s campaign. The former NFL star has been accused of repeatedly threatening his ex-wife’s life, exaggerating claims of financial success and overstating his role in a for-profit program alleged to have preyed on veterans and service members while defrauding the government.

Earlier this year, after a story by the Beast, Walker acknowledged the existence of three children he had not previously talked about.

The woman told the Beast for Wednesday’s story that his denial of the abortion was somewhat surprising to her.

“Sure, I was stunned, but I guess it also doesn’t shock me, that maybe there are just so many of us that he truly doesn’t remember,” the woman said. “But then again, if he really forgot about it, that says something, too.”

In the Beast report published late on Monday, the outlet said it reviewed a receipt showing the woman’s payment for the procedure, along with a get-well card from Walker and bank deposit records showing a $700 personal check from Walker dated five days after the abortion receipt.

During the Republican primary, Walker backed a national ban on abortions with no exceptions for cases involving rape, incest or a woman’s health being at risk – particularly notable at a time when the 1973 Roe v Wade supreme court precedent had been overturned and Democrats in Congress were discussing codifying abortion rights.

“I’m for life,” Walker has said repeatedly. Asked about whether he would allow for any exceptions, he has said there are “no excuses”.

As the Republican nominee, Walker has sometimes sidestepped questions about his earlier support for a national abortion ban, a tacit nod to the fact that most voters, including many Republicans, want at least some legal access to abortion.