James Comey has apparently asked the US Justice Department to publicly refute Mr Trump’s accusations – a move which questions the President’s truthfulness.
His intervention follows comments from James Clapper – the director of national intelligence in the Obama administration – who denied there was an order for surveillance at Trump Tower.
In an interview with NBC’s Meet The Press, Mr Clapper said that in the national intelligence work he oversaw, there was “no such wiretap activity mounted against the President, the President-elect at the time, as a candidate or against his campaign”.
Mr Clapper, who left the White House on 20 January when Mr Trump took office, said he would have known about such an order.
“Absolutely, I can deny it,” he said.
The White House has requested Congress investigate Mr Trump’s accusation that his predecessor ordered a wiretap of the phones at Trump Tower – his New York residence and campaign headquarters – before the November election.
Mr Trump has not offered any evidence to support his claims, and Mr Obama has rejected the allegations, with a spokesman describing them as “simply false”.
White House press secretary Sean Spicer said in a statement on Sunday: “Reports concerning potentially politically motivated investigations immediately ahead of the 2016 election are very troubling.”
He said the President had requested “that as part of their investigation into Russian activity, the congressional intelligence committees exercise their oversight authority to determine whether executive branch investigative powers were abused in 2016”.
It was unclear which reports Mr Spicer was referring to, but the House Intelligence Committee said it “will make inquiries” into the accusations.
Senator Tom Cotton, a Republican member of the Senate Intelligence Committee, said his panel will also look at the allegations as part of its investigation into Russian interference in the presidential election.
The Democratic leader in the House of Representatives, Nancy Pelosi, said Mr Trump’s claims were “just ridiculous”.
She said having people “talking about what you want them to be talking about” was a “tool of an authoritarian”.
Mr Trump made the allegations against Mr Obama in a series of tweets on Saturday, amid growing scrutiny of his campaign’s ties with Russia.
He wrote: “Terrible! Just found out that Obama had my ‘wires tapped’ in Trump Tower just before the victory. Nothing found. This is McCarthyism!”
A spokesman for Mr Obama has dismissed the claims, insisting it was “a cardinal rule” of his administration that no White House official ever interfered with any independent investigations led by the Department of Justice.
Under US law, a federal court would have to have found probable cause that the target of the surveillance is an “agent of a foreign power” before authorising such an order.