In a series of tweets on Saturday, Trump claimed without evidence that his predecessor had tapped the telephones at Trump Tower.
Obama’s director of national intelligence said no such action was carried out against the New York businessman as a candidate or against his campaign.
An Obama spokesman has said Trump’s accusation was “simply false.”
Lawmakers from both parties appealed for Trump to provide proof for the startling claim, yet the White House said there would be no further comment until “such oversight is conducted” by the congressional intelligence committees.
House Democratic leader Nancy Pelosi said: “It’s called a wrap-up smear. You make up something. Then you have the press write about it.
“And then you say, everybody is writing about this charge. It’s a tool of an authoritarian.”
White House press secretary Sean Spicer announced the request for a congressional inquiry in a statement that referred to “very troubling” reports “concerning potentially politically motivated investigations immediately ahead of the 2016 election.”
Trump said the wiretapping happened in October at the New York skyscraper where he ran his campaign and transition.
Spicer said the White House wants the committee to “exercise their oversight authority to determine whether executive branch investigative powers were abused in 2016.”
Spicer’s chief deputy, Sarah Huckabee Sanders, said she thinks Trump is “going off of information that he’s seen that has led him to believe that this is a very real potential.”
Josh Earnest, who was Obama’s press secretary, said that presidents do not have authority unilaterally to order the wiretapping of American citizens.
FBI investigators and justice department officials must seek a federal judge’s approval to investigate by demonstrating that probable cause exists.
Earnest accused Trump of levelling the allegations to distract from the attention being given to campaign season contacts by Trump aides with a Russian official, including campaign adviser Jeff Sessions before he resigned from the Senate to become attorney-general. The FBI is investigating those contacts, as is Congress.
Devin Nunes, chairman of the house intelligence committee, said in a statement that the committee “will make inquiries into whether the government was conducting surveillance activities on any political party’s campaign officials or surrogates.”
The committee’s top Democrat, Adam Schiff of California, said Trump was following “a deeply disturbing pattern of distraction, distortion and downright fabrication”.
Trump’s call for Congress to investigate Obama has risks, though, particularly if damaging information about him or his associates is uncovered. Lawmakers are promising to follow the evidence wherever it takes them.
In his tweets, Trump compared the alleged wiretapping to “Nixon/Watergate” and “McCarthyism!” And he called Obama a “Bad (or sick) guy.”
Trump said in the tweets that he had “just found out” the information, though it was unclear whether he was referring to a briefing, a conversation or a media report.
The president in the past has tweeted about unsubstantiated and provocative reports he reads on blogs or conservative websites.
Trump spoke recently about how much he likes Obama and how much they get along, despite their differences.