"There's no question that something happened. The question is it, is it surveillance, is it a wiretap or whatever?" Spicer said during an off-camera briefing at the White House. "There has been enough reporting that strongly suggesting something occurred."
Spicer, who declined to identify any specific piece of evidence to support Trump's claim, said the President asked Congress to investigate based on those unnamed reports.
"There's enough out there now that makes one wonder how some of this happened without the existence of surveillance," Spicer said.
His remarks came a day after the White House said Trump would request the investigation from lawmakers. Spicer wrote in a statement Sunday that "neither the White House nor the President will comment further until such oversight is conducted."
In his tweets, Trump alleged that former President Barack Obama had ordered his phones tapped in October, in the final weeks of the presidential election.
Sources told CNN over the weekend that Trump made the claim after an article on the subject from the conservative website Breitbart circulated among White House staffers.
In his briefing Monday, Spicer wouldn't name a specific source for Trump's information. And he would not commit to accepting the results of the congressional probe.
"I don't think you would ever just say I'll accept any outcome," Spicer said. "If we have a problem with the conclusions we'll let it be known."
Spicer said Trump was also requesting lawmakers investigate national security leaks that he argues are meant to undermine his presidency.
Trump believes "pervasive leaks" undermine the nation's security and wants legislative investigative bodies to examine them, his spokesman said.
Administration sources have suggested that Trump and his top aides are wary of Obama-era officials who they believe are leaking sensitive information meant to make Trump look bad.
Despite those accusations, Spicer predicted Monday that the relationship between Obama and Trump would remain functional.
"I think that they'll be just fine," Spicer said.