The president told Fox News a “wiretap covers a lot of different things” and hinted more could emerge in the coming weeks.
Barack Obama has denied the charge and former spy chiefs and several lawmakers have said they have seen no evidence.
The latest senior figure to cast doubt on the allegation was the Republican chairman of the House intelligence committee, Devin Nunes.
He said on March 15 he doesn’t believe “there was an actual tap of Trump Tower”.
Earlier this month, President Trump tweeted that President Obama had wiretapped his phones during the presidential campaign.
In a series of tweets, Donald Trump accused his predecessor directly, asking: “Is it legal for a sitting President to be <<wire tapping>> a race for president?”
Talking to Fox News in an interview that was broadcast in full on March 15, he made his first comments about the wiretap accusation he made two weeks ago.
Donald Trump said: “Wiretap covers a lot of different things. I think you’re going to find some very interesting items coming to the forefront over the next two weeks.”
Despite repeated requests from reporters, the White House has not provided any evidence to support his claim.
White House Press Secretary Sean Spicer has said President Trump “used the word <<wiretap>> in quotes to mean broadly surveillance and other activities”.
Sean Spicer also said that President Trump was not accusing Barack Obama personally.
Donald Trump asked Congress to examine the allegation as part of an investigation into alleged Russian meddling in last year’s election.
Senator Lindsey Graham, who is leading the Senate Judiciary Committee’s investigation of allegations of Trump-Russia ties, has pressed the FBI to come forward with more details of its own probe into the issue.
Lindsey Graham said on March 15 he would use a court order to force FBI Director James Comey to submit details on its Russian investigation and whether there was any evidence of Donald Trump’s phones being wiretapped.
James Comey promised on March 15 to provide answers in a classified briefing.
Intelligence agencies found that Russia conducted cyber-attacks against the Democratic Party as part of an effort to influence the election in Donald Trump’s favor.
Russia has repeatedly denied any involvement.
Donald Trump has been dogged by claims that his advisers and staff had ties to Russian officials, but there has been no evidence of any collusion between his campaign and Moscow.
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