Deputy White House press secretary Sarah Huckabee Sanders, appearing Sunday on ABC's This Week, reiterated calls for an investigation.
"All we're saying is let's take a closer look", she said.
EARNEST: And the bigger the scandal, the more outrageous the tweet.
He made the allegations in a series of tweets claiming he "just found out that Obama had my "wires tapped" in Trump Tower just before the victory".
The senators sent a similar letter on Monday to William Callahan, deputy director of the U.S. Secret Service, asking how the agency will conduct background checks on people who will be present during Trump's trips to Mar-a-Lago, Trump Tower in New York City, Trump's golf resort in Bedminster, New Jersey, or other Trump properties where he may conduct official business.
Chris Coons, the Democratic Senator from DE, called the allegations made by Trump "remarkable", saying that, "I think another attempt by President Trump to change the subject".
"We are in the midst of a civilization-warping crisis of public trust", said Sen. Neither the White House nor Obama's office has responded immediately to NPR's requests for comment. As part of that practice, neither President Obama nor any White House official ever ordered surveillance on any USA citizen.
While Trump spent years asserting the falsehood that Obama was born outside the US, he had recently become more conciliatory about his predecessor.
He said they had a "cardinal rule" that "no White House official ever interfered with any independent investigation led by the Department of Justice".
Coons (pictured below) noted that he does not think any president should ever "directly order an intercept or wiretap of an American citizen".
The New York Times in October said the FBI was investigating Russia's possible role in the USA campaign, and said agents had scrutinized advisers close to Trump for any connections to Russian financial figures.
"What do the Russians have on Donald Trump?" she said during an appearance on CNN's "Face the Nation".
Mukasey, who served as the attorney general under former President George W. Bush, said he believes there was surveillance on Trump Tower after reading certain news reports.