Obama denies Trump's unsubstantiated claim that he wiretapped phones in Trump Tower

— -- A spokesman for former President Obama issued a strong denial to President Trump's unsubstantiated accusation that the former commander-in-chief wiretapped Trump Tower phones during the election campaign.

"A cardinal rule of the Obama administration was that no White House official ever interfered with any independent investigation led by the Department of Justice," Obama spokesman Kevin Lewis said in a statement Saturday. "As part of that practice, neither President Obama nor any White House official ever ordered surveillance on any U.S. citizen. Any suggestion otherwise is simply false."

The former president was responding to a series of tweets Saturday morning by Trump claiming that Obama wiretapped phones in Trump Tower in New York City during the presidential campaign.

Trump offered no proof for his claims. ABC News has asked the White House for comment but has yet to receive a response.

The president's tweets came after an article ran Friday on the right-wing news site Breitbart claiming that the Obama administration obtained authorization to eavesdrop on the Trump campaign.

Trump in his posts compared the alleged wiretapping to the Watergate scandal under former President Nixon.

He also suggests the possibility of a legal case over the alleged wiretapping.

Later in the morning, Obama's former deputy national security adviser, Ben Rhodes, used Twitter to challenge Trump's claims.

"No president can order a wiretap," Rhodes, who continues to serve as a foreign-policy adviser to Obama post-presidency, said in one tweet. "Those restrictions were put in place to protect citizens from people like you."

In response to Trump's suggestion that a good lawyer could make the case that Obama tapped his phones, Rhodes tweeted, "No. They couldn't. Only a liar could do that."

Republican Lindsey Graham, who has at times been critical of Trump, mentioned the president's claims during a packed town hall Saturday in the senator's home state of South Carolina.

"I am very worried," Sen. Graham told the crowd. "I'm very worried that our president is suggesting that the former president has done something illegal. I would be very worried if, in fact, the Obama administration was able to obtain a warrant lawfully about Trump campaign activity with a foreign government. So it's my job as the United States senator to get to the bottom of this. I promise you I will."

Democrats in Congress also weighed in.

Rep. Eric Swalwell of California commented on the president's accusation against Obama during an interview on "Fox & Friends."

"First, look, presidents do not wiretap anyone," the Democratic representative said. "These are pursued by the Department of Justice in accordance with the FBI and signed off by a judge."

The congressman continued that "President Trump is not credible when it comes to talking about Russia ... So at this point we don't know what's true and what’s not. I’m on the [House] Intelligence Committee. Our committee is pursuing its own investigation into prior Trump administration-team ties with Russia. But at this point I think this is just the president up early doing his routine tweeting."

House Minority Leader Nancy Pelosi suggested in a tweet that the president was trying to deflect attention from questions surrounding contacts between members of his election campaign and Russia.

“The Deflector-in-Chief is at it again," the California Democrat tweeted. "An investigation by an independent commission is the only answer.”

Oregon Sen. Ron Wyden raised the question in a tweet of whether the president had gotten information from the FBI about its investigation of Russian contacts with Trump campaign associates, or whether "Trump is making it up."

"Either way Americans deserve an explanation," the Democratic senator wrote.