"Terrible! Just found out that Obama had my 'wires tapped' in Trump Tower just before the victory. Nothing found. This is McCarthyism!" Trump tweeted early Saturday morning in one part of a six-tweet tirade that began just after 6:30 a.m.
The President went on to compare the alleged tapping of his phones to Watergate and called Obama "bad (or "sick)."
"How low has President Obama gone to tap my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy," Trump tweeted.
The White House did not provide evidence to back up Trump's claim or explain the source of his information.
But two former senior US officials quickly dismissed Trump's accusations out of hand.
"Just nonsense," said one former senior US intelligence official.
Another former senior US official with direct knowledge of investigations by the Justice Department under the Obama administration said Trump's phones were never tapped.
"This did not happen. It is false. Wrong," the former official told CNN.
A spokesman for Obama, Kevin Lewis, called "any suggestion" that Obama or any White House official ordered surveillance against Trump "simply false."
"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," Lewis said in a statement early Saturday afternoon. "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."
Warrants to tap into someone's phones in the course of a federal investigation would be sought by the Department of Justice, which conducts investigations independent of the White House and the president.
The Foreign Intelligence Surveillance Court, an independent and secretive federal court, is responsible for issuing surveillance warrants in cases concerning foreign intelligence. The FBI has been investigating contacts between Trump campaign advisers and Russians known to US intelligence, and that court would likely be the forum to petition for such a warrant.
The former senior US official with direct knowledge of the Justice Department's investigations said Obama could not have ordered such a warrant. It would have been taken to a judge by investigators, but investigators never sought a warrant to monitor Trump's phones, the former official said.
A federal judge would only have approved a warrant to wiretap Trump's phones if he or she had found probable cause that Trump had committed a federal crime or was a foreign agent.
Former Obama deputy national security adviser Ben Rhodes echoed the point in a tweet responding to Trump on Saturday morning.
"No President can order a wiretap. Those restrictions were put in place to protect citizens from people like you," he said in his Twitter post.
A senior administration official in Washington said colleagues learned of the tweet storm about Obama only after Trump sent them. They were not expecting the President to make any news this morning before golfing in Palm Beach, Florida.
The official said they don't believe Trump is trying to get ahead of any particular story that's about to come out, but rather he is furious about how the Russia storyline is playing out.
The official pointed to a story on the conservative website Breitbart News that was circulating in the West Wing, which followed up on comments from radio talk show Mark Levin claiming Obama worked to undermine Trump's presidential campaign and his administration, including various investigations on Russia and possible ties between Russians and Trump associates.
That story infuriated him, the official said.
Trump's tweets came two days after his attorney general, Jeff Sessions, recused himself from any investigation related to the Trump campaign. Some Democrats have continued to call for Sessions' resignation after he acknowledged meeting multiple times with the Russian ambassador to the US during the campaign despite denying any contacts during his Senate confirmation hearing.
Trump's tweets Saturday morning are just the latest in a string of wild accusations he has made since taking office that either directly contradicted the facts or lacked evidence to substantiate his claims, and they come just days after Trump was widely praised for the unifying tone of his joint address to Congress.
While past presidents have spoken prudently about sensitive matters to ensure that any claims they make are backed up by carefully vetted facts, Trump has instead maintained his pre-presidency style: one defined by unsubstantiated claims bellowed off the cuff or tweeted at odd hours of the day.
Trump has made dozens of verifiably false or misleading claims since taking office, often with an eye on gaining a political advantage or blunting criticism.
The President has repeatedly trumpeted the debunked claim that millions of illegal votes were cast in the 2016 election and accused journalists of inventing a rift between him and the US intelligence community, despite his own statements to that effect.
And last month, he accused a Democratic senator of misrepresenting his Supreme Court nominee's criticism of him, even after the nominee's White House-appointed spokesman corroborated the senator's account of the conversation.
Meanwhile, Trump and his advisers have falsely accused the media of leading a "fake news" campaign to smear his presidency, all the while arguing in favor of "alternative facts."
Sen. Lindsey Graham, a South Carolina Republican who has been critical of Trump, said during a town hall forum Saturday that he didn't know if Trump's claim was true, but said he was "very worried" about the allegation.
"I'm very worried. I'm very worried that our President is suggesting that the former President's done something illegally," Graham said. "I would be very worried if in fact the Obama administration was able to obtain a warrant lawfully about Trump campaign activity with foreign governments. So it's my job as a United States senator to get to the bottom of this. I promise you I will."
California Rep. Adam Schiff, the ranking member of the House Intelligence Committee, which is also probing the scope of Russia's influence on the US election, said in a statement Saturday afternoon in reference to one of Trump's tweets: "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.
"No matter how much we hope and pray that this President will grow into one who respects and understands the Constitution, separation of powers, role of a free press, responsibilities as the leader of the free world, or demonstrates even the most basic regard for the truth, we must now accept that President Trump will never become that man," Schiff said.
Amid criticism that Trump's allegations were meritless, one GOP senator called on Trump to release proof about his accusation, saying the President's allegations were "very serious."
Nebraska Sen. Ben Sasse, a frequent Trump critic, said the President should publicly release the FISA Court order that would have been needed if his phones were legally tapped by the government.
And, if Trump believes his phones were illegally monitored, he "should explain what sort of wiretap it was and how he knows this," Sasse said in a statement.
"We are in the midst of a civilization-warping crisis of public trust, and the President's allegations today demand the thorough and dispassionate attention of serious patriots," Sasse said. "A quest for the full truth, rather than knee-jerk partisanship, must be our guide if we are going to rebuild civic trust and health."
This story has been updated to reflect new developments.
CNN's Eugene Scott, Jim Sciutto and Jason Hanna contributed to this report