Instead, Trump, standing alongside German Chancellor Angela Merkel, whose cellphone had been tapped by the Obama administration, said at a news conference: "As far as wiretapping, I guess, by this past administration, at least we have something in common, perhaps".
Graham, of SC, is leading one of three congressional investigations into Russia's interference in the 2016 election.
On Thursday, leaders of the Senate Intelligence committee said in a statement there is no indication that Trump Tower was "the subject of surveillance" by the US government before or after the 2016 election.
Their respective counterparts on the House of Representatives Intelligence Committee, Devin Nunes and Adam Schiff, made similar comments on Wednesday, Efe news reported.
"They are not findings", he said.
Trump was referring to a disclosure in 2013 by former NSA contractor Edward Snowden that the US had conducted spying operations in Germany, including the monitoring of Merkel's cellphone.
Identities of Americans who show up in US surveillance against foreign targets are generally concealed, but can be unmasked by intelligence agencies in certain circumstances.
White House press secretary Sean Spicer continued to defend President Donald Trump's claims that he was put under surveillance by his predecessor Barack Obama during the 2016 election, even as fellow Republicans said there is no evidence.
Russia Claims: No Evidence Of Collusion - Nunes
Nunes also said ahead of Monday's hearing he had seen "no evidence" of collusion between Russian Federation and Trump's team. Trump is facing increased pressure in Congress to back down from the wiretapping claims he made on Twitter March 4.
The bipartisan committee issued a statement earlier this week to that effect, saying it sees "no indications" that Trump was wiretapped.
"I strongly believe that these statements by political leaders should not be a substitute for a public response from the Federal Bureau of Investigation and Department of Justice on this matter", said Sen.
Meanwhile, Rep. Elijah Cummings, D-Maryland, released documents last Thursday that show Mr. Trump's former national security adviser, Michael Flynn, was paid more than $67,000 from Russian Federation companies before the presidential election.
The top members of the Senate Intelligence Committee also say that they've seen no evidence suggesting Mr. Trump's phones at Trump Tower were tapped by Obama.
Sens. Chuck Grassley of Iowa and Dianne Feinstein of California sent a letter February 15 to Attorney General Jeff Sessions and Comey asking about the circumstances that led to Flynn's resignation.
Stone said he was unaware at the time that USA officials believed the hacker had ties to Russian Federation. Trump has said he had nothing to do with Russian Federation and described the probes as witch-hunts. Those include situations when the communications contain information that a crime has or is about to be committed, when the Americans' identity is necessary to understand the importance of the foreign intelligence collected or when the communication provides information that an American may be an agent of a foreign power. In a statement to The Associated Press, Stone said he's retained two attorneys to explore whether he can compel the government to "either charge me or admit they have no case whatsoever". Stone communicated through Twitter direct messages with Guccifer 2.0, a hacker who has claimed responsibility for breaching the Democratic National Committee.