U.S. President Donald Trump's attorney Rudy Giuliani said on Sunday he would not rule out the possibility that payments were made to women other than porn star Stormy Daniels to get them to stay silent about accusations against Trump.

Giuliani told ABC's This Week that he had no knowledge of whether former Trump attorney Michael Cohen had other payments but he said, "I would think if it was necessary, yes. He [Cohen] made payments for the president or he's conducted business for the president."

Giuliani called the $130,000 US Cohen paid to Daniels in 2016 a "nuisance payment." Daniels alleges that she had a sexual encounter with Trump in 2006. Trump has denied Daniels's allegations.

Cohen, Trump's longtime personal lawyer, faces a criminal investigation in part over the payment to Daniels, whose real name is Stephanie Clifford.

'Extramarital affair slush fund'

Daniels's lawyer, Michael Avenatti, accused Trump of having an "extramarital affair slush fund" and told ABC he believed similar payments had been made to other women.

Disclosure of additional payments could complicate matters for Trump, who initially denied knowledge that money was paid to Daniels.

Giuliani said on Friday that Cohen's payment to Daniels — one month before the November 2016 presidential election — did not violate campaign laws and would have been made even if Trump were not running.

U.S. President Donald Trump and his lawyer Rudy Giuliani have contradicted each other again about hush money given to adult film star Stormy Daniels. 3:01

During a Fox News interview earlier in the week, Giuliani did link the payment to the presidential campaign and acknowledged for the first time that Trump was aware of the payment. He told the New York Times later that Trump reimbursed Cohen a total of $460,000 or $470,000 after the campaign was over, which he said included "incidental expenses."

Cohen is no longer Trump's attorney, Giuliani said. "It would be a conflict right now for him to be the president's attorney," he told ABC.

Avenatti has said his team has been approached by multiple other women about Trump and he believed evidence would emerge of similar payments.

I would urge the public to watch Mr. Giuliani’s full interview on <a href="https://twitter.com/ThisWeekABC?ref_src=twsrc%5Etfw">@ThisWeekABC</a>. An unmitigated disaster. This is what happens when you can’t keep your lies straight. <a href="https://twitter.com/hashtag/basta?src=hash&ref_src=twsrc%5Etfw">#basta</a> <a href="https://t.co/kuWTjkLT5B">https://t.co/kuWTjkLT5B</a> —@MichaelAvenatti

"The president had effectively an extramarital affair slush fund that was administered by Michael Cohen and that he would just be expected to take care of these things," he said on ABC.

"They were a regular occurrence. I mean, that in and of itself should be very disturbing."

Senior White House adviser Kellyanne Conway said she was not aware of any other possible payoffs. "They didn't cross my desk as campaign manager," she told CNN's State of the Union.

'Fast moving' exchange

Trump told reporters last month on Air Force One he did not know about the payment to Daniels. Conway said Trump meant to say he did not know about the payment at the time it was made.

"The 'no' refers to when the payment occurred," she told CNN. "It was a fast-moving exchange. I asked the president what he meant and he said, 'I didn't know about it when the payment occurred.'"

U.S. Representative Adam Schiff, the top Democrat on the House intelligence committee, said the shifting story on when Trump knew was problematic.

"The legal problem for the president is telling false statements about this is evidence of a consciousness of guilt," Schiff told CNN. "Seemed abundantly clear he was denying knowledge of this payment, both past and present. Why would he be doing that unless he was aware that what he had done was wrong, what he had done was a violation of campaign law?"