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By Peter Alexander., Kristin Donnelly and Ali Vitali

Former President Barack Obama "rolled his eyes" at President Donald Trump's unsubstantiated claims that he wiretapped Trump Tower at the end of the 2016 election, a source close to the former president tells NBC News.

The source, who spoke to NBC News on the condition of anonymity and is familiar with the president's thinking, said Obama believes the claims "undermine the integrity of the office of the president," but don’t undermine his own integrity, because “he didn’t do it.”

The source told NBC News the former president "is much more concerned by President Trump kicking people off their health insurance, not staffing the government, not being prepared for a crisis, rolling back regulations so that corporations can pollute the air and water and letting mentally unstable people buy guns with no problems whatsoever."

Related: White House Calls for Probe, Offers No Proof of Wiretapping

"He cares about all those things much more than what President Trump tweets at the TV each morning."

Trump tweeted on Saturday that President Obama wiretapped phones in Trump Tower as the days of the presidential election waned. The White House has said Trump supports a congressional investigation into "whether executive branch investigative powers were abused in 2016" as part of a larger investigation into Russian hacking.

Another source with firsthand knowledge told NBC News that Trump's tweets were a matter of concern for the former president.

Obama wanted to be sure that it was unequivocal that he didn't do what Trump alleged, the source told NBC News.

Related: FBI Director Comey Asked Justice Department to Reject Trump’s Wiretap Claims

Trump and Obama have not spoken since the inauguration, the source told NBC News, adding that that they were supposed to connect, but their schedules didn't align.

In the meantime, Senators Lindsey Graham, R-South Carolina, and Sheldon Whitehouse, D-Rhode Island, who sit on that chamber's Judiciary Committee, sent a letter on Wednesday to the FBI director and Acting Deputy Attorney General asking for information on any possible wiretapping of President Trump, the Trump campaign or Trump Tower.

The request asks specifically for copies of warrant applications or court orders relevant to the alleged wiretaps.

"We would take any abuse of wiretapping authorities for political purposes very seriously," the lawmakers wrote. "We would be equally alarmed to learn that a court found enough evidence of criminal activity or contact with a foreign power to legally authorize a wiretap of President Trump, the Trump Campaign, or Trump Tower."