Neither Breitbart News nor Levin provided any independent reporting to back up the assertions and Trump's White House didn't respond to requests for an on-the-record account of Trump's allegations.
"A cardinal rule of the Obama administration was that no White House official ever interfered with any independent investigation led by the Department of Justice," Kevin Lewis, a spokesman for Obama, said in an emailed statement on Saturday. "As part of that practice, neither President Obama nor any White House official ever ordered surveillance on any US citizen. Any suggestion otherwise is simply false."
Ben Rhodes, Obama's former deputy national security adviser, also denied Trump's claims on Saturday. "No President can order a wiretap," Rhodes wrote on Twitter in a response back to Trump. "Those restrictions were put in place to protect citizens from people like you."
Trump is spending the weekend at his Mar-a-Lago resort in Palm Beach, Florida. He is scheduled to attend a National Security Council briefing Saturday afternoon after golfing.
After recent news stories highlighted a number of meetings between Trump associates and Russian government officials during the 2016 election, Trump has trained his Twitter account on top Democrats, seeking to highlight their actions instead.
Comparing Obama to former President Richard Nixon during the 1970s Watergate scandal, Trump took his long-running feud with his predecessor to a new level in four separate early-morning tweets to his almost 26 million followers.
"Is it legal for a sitting President to be 'wire tapping' a race for president prior to an election? Turned down by court earlier. A NEW LOW!," one tweet said. "How low has President Obama gone to tapp my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!"
The tweets were issued two days after Attorney General Jeff Sessions said he'd recuse himself from any investigations into possible ties between the Trump campaign and the Russian government.
House Minority Leader Nancy Pelosi reiterated her calls for an independent investigation into the Trump campaign's ties to Russia. "The Deflector-in-Chief is at it again," Pelosi wrote Saturday on Twitter. "An investigation by an independent commission is the only answer."
The New York Times in October said the FBI was investigating Russia's possible role in the US campaign, and said agents had scrutinized advisers close to Trump for any connections to Russian financial figures. The newspaper, in an October 31 story, said the FBI pursued the possibility of a secret channel of email communication from the Trump Organization to a Russian bank. The Times said the FBI "came to doubt" such a channel existed.
Levin, a former Reagan administration aide, highlighted news stories by the Times and other media outlets as he asserted on Thursday that the Obama administration put the Trump campaign under surveillance. "The question is: Was Obama surveilling top Trump campaign officials during the election?" Levin asked. "We absolutely know this is true."
Breitbart's follow-up on Friday referred to Levin's claims and outlined a number of published news accounts, dating back to June 2016, about alleged actions taken against Trump by intelligence agencies under Obama.
Democrats and some Republicans have called for further scrutiny into links between the Trump team and the Russian government during the 2016 election. Lawmakers from both parties called for Sessions to recuse himself after news reports showed that he met with the Russian ambassador to the US, Sergey Kislyak, twice last year, after denying meeting with Russian officials in testimony during his Senate confirmation hearing. Top Democrats called for Sessions - who said the meetings were not campaign-related - to resign.
News reports found that other Trump associates, including Carter Page, an energy consultant and foreign policy adviser, had met with Kislyak during the 2016 campaign, contradicting previous statements by the campaign. US intelligence agencies previously determined that Russia directed cyber attacks to meddle in the US election, benefiting Trump.
During a Saturday town hall meeting in Clemson, South Carolina, Republican Sen. Lindsey Graham said an independent commission may be needed to fully uncover Russia's role in the 2016 election and possible ties to Trump.
Referring to Trump's tweets about wiretapping, Graham said that if the claims are true it could be a sign that a court approved such a move because of concerns that the Trump campaign was colluding with the Russians. "I would be very worried if in fact the Obama administration was able to obtain a warrant lawfully about Trump campaign activity with foreign government," he said. "It's my job as the United States senator to get to the bottom of this. I promise you I will."
Trump also said on Twitter that Kislyak visited Obama's White House multiple times last year, and floated the idea of taking legal action against the former president. On Friday he sent tweets deriding previous contacts between Kislyak, Moscow's envoy to Washington since 2008, and Democrats including Pelosi and Chuck Schumer of New York, the top Democrat in the Senate.
"I'd bet a good lawyer could make a great case out of the fact that President Obama was tapping my phones in October, just prior to Election!," he tweeted.
While Trump spent years asserting the falsehood that Obama was born outside the US, he had recently become more conciliatory about his predecessor. "It's a very strange phenomenon. We get along," Trump said in February in an interview with Bill O'Reilly of Fox News. "I don't know if he will admit this, but he likes me. I like him because I can feel it."
- With assistance from Michelle Jamrisko