The allegation – made without showing any evidence – included calling Mr Obama a “bad, or sick, guy”.
Soon after he added: “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!
“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!”
Mr Trump also suggested that Mr Obama was “sick”, writing: “How low has President Obama gone to tapp [sic] my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!”
Mr Obama‘s spokesman denied the allegations, saying any suggestion he or his staff had “ordered surveillance on any US citizen” was false.
Kevin Lewis added that a “cardinal rule” of the Obama administration was that no White House official ever interfered in any Justice Department investigations, which are supposed to be conducted free of political influence.
“As part of that practice, neither Obama nor White House official ever ordered surveillance on any US citizen. Any suggestion otherwise is false,” he said.
Democratic commentators were quick to defend the former President.
Ben Rhodes, a foreign policy adviser to Mr Obama, tweeted: “No President can order a wiretap. Those restrictions were put in place to protect citizens from people like you.”
And Representative Eric Swalwell, who sits on the House Intelligence Committee, told Fox News: “I think this is just the president up early doing his routine tweeting.
“Presidents don’t wiretap anyone. These are pursued by the Department of Justice in accordance with the FBI and signed off by a judge.”
Congressman Ted Lieu added: “Mr President: If there was a wiretap at Trump Tower, that means a fed judge found probable cause of crime which means you are in deep s***.”
The President has a long history of making unfounded and sometimes bizarre claims and it is not the first time he has used them to attack his predecessor.
The tirade came at end of a week in which Mr Trump had been praised widely for acting in a more Presidential fashion, during his first address to Congress.