Trump made the accusation in a series of tweets, without citing evidence, just weeks into his administration and amid rising scrutiny of his campaign's ties to Russia.
"Neither President Obama nor any White House official ever ordered surveillance on any U.S. citizen. Any suggestion otherwise is simply false," Obama spokesman Kevin Lewis said in a statement.
Trump hurled the accusation in the tweets sent early on Saturday morning.
Terrible! Just found out that Obama had my "wires tapped" in Trump Tower just before the victory. Nothing found. This is McCarthyism!— Donald J. Trump (@realDonaldTrump) March 4, 2017
Just out: The same Russian Ambassador that met Jeff Sessions visited the Obama White House 22 times, and 4 times last year alone.— Donald J. Trump (@realDonaldTrump) March 4, 2017
"How low has President Obama gone to tapp my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!," Trump wrote in one tweet. "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!"
Trump said the alleged wiretapping took place in his Trump Tower office and apartment building in New York, but there was "nothing found."
U.S. intelligence agencies concluded last year that Russia hacked and leaked Democratic emails during the election campaign as part of an effort to tilt the vote in Trump's favor. The Kremlin has denied the allegations.
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!— Donald J. Trump (@realDonaldTrump) March 4, 2017
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!— Donald J. Trump (@realDonaldTrump) March 4, 2017
Lewis also said that "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."
The statement did not dismiss the possibility that a wiretap of the Trump campaign could have been ordered by Justice Department officials.
The White House did not respond to a request to elaborate on Trump's accusations.
How low has President Obama gone to tapp my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!— Donald J. Trump (@realDonaldTrump) March 4, 2017
A Trump spokeswoman said the Republican president is "having meetings, making phone calls and hitting balls" at his golf course in West Palm Beach.
Trump's tweets caught his aides by surprise, with one saying it was unclear what the president was referring to.
Members of Congress said Trump's allegations require investigation or explanation.
U.S. Representative Adam Schiff, the top Democrat on the House Intelligence Committee, called Trump's assertion a "spectacularly reckless allegation.
"If there is something bad or sick going on, it is the willingness of the nation's chief executive to make the most outlandish and destructive claims without providing a scintilla of evidence to support them," Schiff said.
Senator Ron Wyden, a Democrat, tweeted, "Either FBI is talking to the subject of an investigation or Trump is making it up. Either way Americans deserve explanation."
Earlier, former Obama adviser Ben Rhodes strongly denied Trump's allegations.
"No president can order a wiretap. Those restrictions were put in place to protect citizens from people like you," Rhodes wrote on Twitter.
Trump's administration has come under pressure from Federal Bureau of Investigation and congressional investigations into contacts between some members of his campaign team and Russian officials during his campaign.
Senator Lindsey Graham, a South Carolina Republican, said he had no knowledge about any wiretapping but is "very worried that our president is suggesting that the former president has done something illegally. I would (also) be very worried if in fact the Obama administration was able to obtain a warrant lawfully about Trump campaign activity."
Graham said it was his job "to get to the bottom of this. I promise I will."
Several other Republicans again urged an investigation into a series of intelligence-related leaks.
House Democratic Leader Nancy Pelosi ridiculed Trump's assertions. "The Deflector-in-Chief is at it again. An investigation by an independent commission is the only answer," she wrote on Twitter on Saturday.
Obama imposed sanctions on Russia and ordered Russian diplomats to leave the United States in December over the country's involvement in hacking political parties in the Nov. 8 U.S. presidential election.
Representative Eric Swalwell, a Democrat who is also a member of the House Intelligence Committee, told Fox News on Saturday that Trump "is not credible when it comes to talking about Russia."
Swalwell downplayed Trump's allegation. "I think this is just the president up early doing his routine tweeting, he said. "Presidents don't wiretap anyone. These are pursued by the Department of Justice in accordance with the FBI and signed off by a judge."
Under U.S. law, a federal court would have to have found probable cause that the target of the surveillance is an "agent of a foreign power" in order to approve a warrant authorizing electronic surveillance of Trump Tower.
Several conservative news outlets and commentators have made similar allegations in recent days about Trump being wiretapped during the campaign, without offering any evidence.
Trump's national security adviser, Michael Flynn, resigned in February after revelations that he had discussed U.S. sanctions on Russia with the Russian ambassador to the United States before Trump took office.
Flynn had promised Vice President Mike Pence he had not discussed U.S. sanctions with the Russians, but transcripts of intercepted communications, described by U.S. officials, showed that the subject had come up in conversations between him and the Russian ambassador.
Trump has often used his Twitter account to attack rivals and for years led a campaign alleging that Obama was not born in the United States. He later retracted the allegation.
On Thursday, U.S. Attorney General Jeff Sessions said he would stay out of any probe into alleged Russian meddling in the 2016 presidential election but maintained he did nothing wrong by failing to disclose he met last year with Russia's ambassador to the United States.
Trump has accused officials in Obama's administration of trying to discredit him with questions about Russia contacts.
Trump called frequently during his campaign for improved relations with Russia, drawing criticism from Democrats and some Republicans.
Ties with Russia have been deeply strained in recent years over Moscow's military interference in Ukraine, military support for President Bashar al-Assad in Syria and President Vladimir Putin's intolerance of political dissent.
Banner and thumbnail credit: Reuters, Kevin Lamarque