Washington (CNN) Sen. John McCain said Sunday that President Donald Trump should either retract or substantiate his claim that President Barack Obama wire-tapped him in the final weeks of the presidential campaign and added he expects more to come on Russia's meddling in the US election.

McCain said on CNN's "State of the Union" that he had "no reason to believe" Trump's allegation, which the President has not supported with any evidence and which a White House official said was prompted by a Breitbart article.

"I have no reason to believe that the charge is true, but I also believe that the President of the United States could clear this up in a minute," McCain told anchor Jake Tapper. "All he has to do is pick up the phone, call the director of the CIA, director of national intelligence and say, 'OK, what happened?'"

The Arizona senator's comments marked the latest high-profile call for the President to explain a series of tweets he sent on March 4 in which he claimed, without evidence, that Obama had the "wires tapped" at Trump Tower. Since Trump leveled the stunning accusations, several current and former national security officials denied the accusation, including former Director of National Intelligence James Clapper, as did Obama himself through his spokesman. Sources have told CNN that FBI Director James Comey also pushed back against Trump's claim.

Under the Foreign Intelligence Surveillance Act, law enforcement agencies must obtain a warrant from a secret court to undertake such monitoring. But communications of Americans may be swept up in the monitoring of foreigners, as was reportedly the case with ex-national security adviser Michael Flynn, whose leaked contacts with Russian diplomat Sergey Kislyak led to his ouster.

Reports that Trump's associates contacted Russians known to US intelligence during the campaign have dogged Trump for months, raising questions about whether those contacts had anything to do with Russia's meddling in the US election. The US intelligence community has concluded that Moscow launched an aggressive hacking campaign to undermine the candidacy of Democratic nominee Hillary Clinton.

The Russian government has denied these claims, with Kremlin spokesman Dmitry Peskov telling CNN's Fareed Zakaria in an interview that aired Sunday: "Russia is being demonized."

Facing political pressure over reports that he, too, met with Kislyak but did not acknowledge it during his confirmation hearing, Attorney General Jeff Sessions announced earlier this month that he would recuse himself from any investigation into Trump's campaign.

The House and Senate Intelligence committees have said they are investigating alleged Russian involvement in the election, and the White House has asked Congress to include Trump's unsubstantiated wiretapping claims in its investigations.

House Speaker Paul Ryan said on CBS "Face the Nation" in an interview that aired Sunday that he had not seen any evidence to back Trump's claims. Ryan is a member of the "Gang of Eight" of congressional leaders with access to the nation's top intelligence. FBI Director James Comey met behind closed doors with those lawmakers Thursday.

In his interview Sunday, McCain said Trump's accusation must be resolved; if left hanging, "it undermines the confidence the American people have in the entire way the that the government does business," he said.

McCain also expressed his concern with the mounting questions about the relationships between Russian officials and people tied to Trump, who advocated for better relations with Russia during the campaign.

"There's a lot of aspects of this whole relationship with Russia and (Russian President) Vladimir Putin that requires further scrutiny, and so far, I don't think the American people have gotten all the answers,"McCain said. "In fact, I think there's a lot more shoes to drop from this centipede."

McCain, who has advocated a hard line against Russia, called into question the failure of the Republican Party to adopt at its 2016 national convention a plank for the provision of defensive weapons to Ukraine following Russia's invasion of Crimea.

"Why was that taken out of the Republican platform?" McCain asked. "Clearly, it was not the will of most Republicans."

As president, Obama weighed the idea of arming Ukraine, but ultimately did not proceed with such a move.

McCain named Flynn as one person about whom he had questions. He went on to say that former Trump adviser Roger Stone also needed to be questioned in addition to former Trump campaign manager Paul Manafort, accusing both of questionable ties to the ousted Ukrainian President Viktor Yanukovych. Stone expressed an openness Monday to testifying before Congress about his "nonexistent Russian contacts."

"This whole issue of the relationship with the Russians and who communicated with them and under what circumstances clearly cries out for investigations, but I would also point out, we should not assume guilt until we have a thorough investigation," McCain said.

This story has been updated.