President Trump’s accusation that former President Obama tapped his telephones during the 2016 presidential race and his call Sunday for Capitol Hill investigations into the matter received qualified support from the GOP leaders of Congress’ top intelligence panels.

Rep. Devin Nunes, R-Calif., chairman of the House Intelligence committee, indicated strongly that his panel would look into the matter.

“One of the focus points of the ... committee's investigation is the U.S. government's response to actions taken by Russian intelligence agents during the presidential campaign," he said. "As such, the committee will make inquiries into whether the (U.S.) government was conducting surveillance activities on any political party’s campaign officials or surrogates."

However, Sen. Richard Burr, R-N.C., the head of the Senate Select Committee on Intelligence, offered a more measured response.

“As I’ve said since the beginning and have repeated since, the … committee on Intelligence will follow the evidence where it leads," he said. "And we will continue to be guided by the intelligence and facts as we compile our findings.”

Over his two terms of office, Obama had a strained relationship with Russian President Vladimir Putin, in large part over problems in Ukraine and Syria.

The issue of whether Russia interfered with the 2016 White House race began to percolate soon after Trump joined the GOP primary in June 2015. Candidate Trump repeatedly praised Putin’s strong leadership style, including what he considered Putin’s ability to outmaneuver Obama.

The matter exploded last summer after computers connected to the Democratic National Committee and the campaign of Democratic presidential nominee Hillary Clinton were hacked.

The U.S. intelligence committee concluded that Russia indeed meddled in the race but found no evidence of voter fraud.

Subsequent revelations about conversations between people associated with the Trump campaign and Russian Ambassador Sergey Kislyak have led to the resignation of National Security Adviser Michael Flynn and the recusal of Attorney General Jeff Sessions from any probe into Russian involvement into the U.S. political system, though no proof of wrongdoing has surfaced.

Trump was reportedly furious about Sessions's recusal last week. By early Saturday the president had fired off a series of tweets in which he accused Obama of ordering the wiretaps at Trump Tower, his official campaign headquarters. Trump suggested such an act was tantamount to “McCarthyism” and rasied the specter of “Nixon/Watergate.”

“Is it legal for a sitting president to be ‘wire tapping’ a race for president prior to an election?” Trump said the tweets. “How low has President Obama gone to tap (sic) my phones during the very sacred election process.”

Trump based his allegations on a recent Breitbart News story and comments by conservative talk-show host Mark Levin, but has yet to provide his own evidence.

On Sunday, White House Press Secretary Sean Spicer issued a statement in part saying such reports are “very troubling” and that Trump wants congressional intelligence committees, as part of their investigations into Russian activity, “to determine whether executive branch investigative powers were abused in 2016.”

Congressional Democrats, who have called for a special prosecutor into the entire Russian matter, did not support Trump’s wiretap claims.

"For a president of the United States to make such an incendiary charge -- and one that discredits our democracy in the eyes of the world -- is as destructive as it was baseless," said Rep. Adam Schiff, D-Calif., the ranking member on the House Intelligence committee.

"If the administration truly believes that President Obama illegally eavesdropped on the Trump campaign and wants our committee to investigate the matter, they should join my call on (FBI) Director James Comey to answer any question put to him that is pertinent to the Russia investigation."

Schiff spoke at about the same time former Director of National Intelligence James Clapper said on NBC’s “Meet the Press” that the part of the intelligence community that he oversaw -- including the FBI -- did not wiretap Trump Tower communications.

Clapper also said he had “no knowledge” of a request for a FISA, or Foreign Intelligence Surveillance Court Act, order for a wiretap, which requires at least some evidence of illegal activity.

An Obama spokesman on Saturday denied the allegations, saying nobody in the former administration ordered surveillance on any U.S. citizen and that “any suggestion otherwise is simply false."

Sen. Tom Cotton, R-Ark., a member of the Senate Intelligence committee, suggested Sunday that the wiretapping allegation would be considered as part of the committee’s larger, Russia-related inquires.

“We’ve already begun an inquiry on the intelligence committee into Russia’s efforts to undermine confidence in our political system,” Cotton told “Fox News Sunday.” “That inquiry is going to be thorough, and we’re going to follow the facts wherever they lead us. And I’m sure that this matter will be a part of that inquiry.”

Cotton also said that he's so far seen no proof that the Trump campaign successfully conspired with the Russian government to defeat Clinton.

“I’ve seen no evidence,” he said Fox. “And, again, I would just say that media reports have gotten pretty far over their skis over this.”

Fox News’ Serafin Gomez contributed to this report.