Senior White House adviser Kellyanne Conway said she was not aware of any other possible payoffs. His responses earlier had been limited to denying knowledge of the transaction when it took place in October 2016, weeks before the presidential election.
Cummings is urging Rep. Trey Gowdy, the Republican chairman of the House Oversight and Government Reform committee, to investigate.
Legal experts have said the revelation that Mr Trump reimbursed Mr Cohen raises new questions, including whether the money represented repayment of an undisclosed loan or could be seen as reimbursement for a campaign expenditure. Giuliani says he doesn't know when Trump knew of the payment.
Michael Avenatti, the attorney who represents Daniels, struck back at Conway. He did not elaborate.
Yet he listed a series of points suggesting the Trump team has given considerable thought to the framework of a potential interview.
"You really care about getting information Mr Manafort can give you that would reflect on Mr Trump and lead to his prosecution or impeachment", he told the prosecution.
Mr Giuliani insisted the president did not know the specifics of Mr Cohen's arrangement with Ms Daniels until recently, telling Fox & Friends on Thursday that the president did not know all the details until "maybe 10 days ago".
Trump attorney Rudy Giuliani's statement that the president might assert his constitutional right against self-incrimination in the Federal Bureau of Investigation probe into the Trump campaign's alleged collusion with Russian Federation during the 2016 presidential election has prompted Trump's opponents to brand the president guilty.
In response Trump said the former New York Mayor was new to the job and that he'll soon "get his facts straight".
The president added that "virtually everything" reported about the payments were wrong.
Trump has previously told reporters he did not know of the payment and did not know where Cohen got the money from.
Other associates of Mr. Trump and Mr. Cohen have denied reimbursement by anyone. This week's news has muddied those waters even more.
Now that the president's legal team has gone on the record saying that Mr. Trump repaid Michael Cohen personally for the $130,000 payment to Daniels, Avenatti said it's clear to the American people "what's going on and it's a cover up". Giuliani's revelation seemed to contradict Trump's past statements.
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