The White House remained firm on Sunday even after Mr. Obama’s office denied ordering a wiretap and James R. Clapper Jr., the former director of national intelligence, said on NBC’s “Meet the Press” that there had been no wiretapping of Mr. Trump or his campaign. James B. Comey, the F.B.I. director, privately asked the Justice Department to issue a statement that Mr. Trump’s claim was false, senior officials said, but the department had not done so as of Sunday evening.

“Everybody acts like President Trump is the one that came up with this idea and just threw it out there,” Sarah Huckabee Sanders, a White House spokeswoman, said on “This Week” on ABC News. “There are multiple news outlets that have reported this. And all we’re asking is that we get the same level of look into the Obama administration and the potential that they had for a complete abuse of power that they’ve been claiming that we have done over the last six months.”

Ms. Sanders pointed to reports in “multiple outlets,” including The New York Times, as the foundation for the allegation. Mr. Levin, the radio host, likewise read from a series of mainstream news reports during an appearance on “Fox & Friends” on Sunday.

“The evidence is overwhelming,” he said. “This is not about President Trump’s tweeting. This is about the Obama administration’s spying, and the question isn’t whether it spied.” He added, “The question is who they did spy on, the extent of the spying — that is, the Trump campaign, the Trump transition, Trump surrogates.”

But the news organizations he and Ms. Sanders cited have not reported that Mr. Obama tapped Mr. Trump’s phones, as the president claimed on Twitter. The Times has reported that several of Mr. Trump’s associates are being investigated for their connections with Russians and that law enforcement agencies have examined intercepted communications. It has not reported that those associates themselves have necessarily been wiretapped, but it has reported surveillance of Russians, which is commonplace.

News outlets have noted that a phone call between Michael T. Flynn, Mr. Trump’s first national security adviser, and Russia’s ambassador to the United States, Sergey I. Kislyak, was monitored, leading to Mr. Flynn’s resignation because his account of the conversation did not match the intercept. It is common for the United States to monitor the communications of Russia’s ambassador.

The Times also reported that before leaving office, Obama officials tried to spread information about Russian meddling in the election and possible links between Russia and Trump associates, in order to leave a trail for government investigators.