He said: "I think there's no question that the Obama administration, that there were actions about surveillance and other activities that occurred in the 2016 election".
"The President was very clear in his tweet that it was, you know, "wiretapping", Mr Spicer said, using his fingers to make a gesture suggesting quotation marks.
In an interview with Bergen Record's Mike Kelly, Conway implied that more sophisticated surveillance techniques may have been used to spy on Trump during the campaign, without providing any sort of evidence.
"I wasn't making a suggestion about Trump Tower", Conway said during the interview Monday.
"And I answered him about surveilling, generally".
Since March 4, when Trump first tweeted the claim, which appeared to originate from right-wing conspiracy theories, Obama as well as several top intelligence officials have denied it, saying there was no such surveillance ordered.
The House Intelligence Committee gave the Department of Justice until Monday to provide evidence of the claim, but on Monday afternoon, the DOJ said it needed more time.
"You can surveil someone through their phones, certainly through their tvs - any number of ways", including "microwaves that turn into cameras", Mrs Conway told the paper.
Trump has never provided evidence to back up his claims and the DOJ in its statement yesterday did not confirm the existence of any documents.
The department had been expected to provide a response by Monday to the House intelligence committee, which has made Trump's wiretapping claims part of a bigger investigation into Russian interference in the 2016 presidential election.
The senator's call for more information follows a request from two leading members of the Senate Judiciary Committee for "copies of any warrant applications and court orders - redacted as necessary. related to wiretaps of President Trump, the Trump Campaign, or Trump Tower". FBI Director James Comey, who reportedly asked the Justice Department to publicly reject Trump's wiretapping accusation, is invited to testify.
"I'm not in the job of having evidence".
The source claimed that the Federal Bureau of Investigation director is upset that Trump's tweets on the issue attempt to make it appear as if the agency acted improperly.
Obama's director of national intelligence, James Clapper, has said that nothing matching Trump's claims had taken place, but that has not quelled speculation that Trump's communications were monitored by the Obama administration.
So Conway went another direction on CNN.
"In fact I don't believe - just in the last week of time, the people we've talked to - I don't think there was an actual tap of Trump Tower".