NSA Deputy Director Richard Ledgett told BBC News in an interview published Saturday that the claim showed "a complete lack of understanding in how the relationship works."
Each side is barred from asking for such prohibited actions, he added.
"Of course they wouldn't do it," Ledgett said. "It would be epically stupid."
Ledgett also said the risks to the United Kingdom in carrying out such an act would outweigh any potential benefits.
"There's a fringe narrative out there that the US and UK and all these other governments are willy-nilly just exploiting every vulnerability in every device they can in order to gather information into a big pile and then root through it for interesting things," he said. "That's not what we do at all."
At a press briefing Thursday, White House Press Secretary Sean Spicer read out allegations originally made by Fox News legal analyst Andrew Napolitano on Tuesday that the United Kingdom's Government Communication Headquarters -- the equivalent of the US National Security Agency -- had spied on Trump.
"Judge Andrew Napolitano made the following statement, quote, 'Three intelligence sources have informed Fox News that President Obama went outside the chain of command (to spy on Trump). He didn't use the NSA, he didn't use the CIA ... he used GCHQ,'" Spicer told journalists.
Spicer's comments from the podium triggered fierce denunciations from many British officials.
On Friday, Spicer told reporters that the Trump administration had no regrets
about citing the uncorroborated Fox News report.
"I don't think we regret anything," Spicer told reporters at a gaggle.
Asked by CNN's Jim Acosta if the administration had apologized to the British government over the matter, Spicer replied, "No, we were just passing on news reports."
A White House official told CNN earlier Friday that national security adviser H.R. McMaster spoke with his British counterpart Thursday after Spicer cited the Fox News report.
The conversation was "cordial" and McMaster described Spicer's comment as "unintentional," the official said. McMaster also told his counterpart that "their concerns were understood and heard, and it would be relayed to the White House."
The official said there were "at least two calls" from British officials Thursday, and the British ambassador to the United States called Spicer to discuss the comment.
White House officials later told CNN that it was British ambassador to the US Kim Darroch and Sir Mark Lyall Grant, national security adviser to Prime Minister Theresa May, who "expressed their concerns to Sean Spicer and Gen. McMaster" in two separate conversations Thursday.
"Mr. Spicer and Gen. McMaster explained that Mr. Spicer was simply pointing to public reports, not endorsing any specific story," one official said.
Spicer spoke to Darroch face-to-face at a White House St. Patrick's Day event, according to a British government official, who described the meeting as "serious" in tone and said it was not cordial.