Officials working on behalf of Donald Trump said they want the congressional committees to determine whether "executive branch investigative powers" were abused in 2016 following the President’s extraordinary claims in a series of tweets on Saturday.
Mr Trump has offered no evidence or details to support his claim, denied by Mr Obama's spokesman.
He made the allegations in a series of tweets claiming he "just found out that Obama had my 'wires tapped' in Trump Tower just before the victory. Nothing found. This is McCarthyism!"
Obama spokesman Kevin Lewis said 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 President Obama nor any White House official ever ordered surveillance on any US citizen," Mr Lewis said, adding that "any suggestion otherwise is simply false".
Mr Trump compared the alleged activity to behaviour involving president Richard Nixon and the bugging of his political opponents.
"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!" he tweeted.
Mr Trump said the wire tapping occurred in October. He ran the presidential campaign largely out of Trump Tower in New York.
The call for an investigation came after clashes broke out as hundreds of people gathered at sites around the US to join rallies backing Mr Trump.