"We are calling on Mr. Comey to come forward and explain what's at issue here," Podesta said, adding the significance of the emails was unclear.
"He might have taken the first step of actually having looked at them before he did this in the middle of a presidential campaign, so close to the voting," Podesta said.
Comey's letter was sent over the objections of Justice Department officials. But those officials did not try to stop the FBI from getting the warrant, a source familiar with the decision said, because they are interested in the FBI moving quickly on the probe.
Sources close to the investigation have said the latest emails were discovered as part of a separate probe of former Democratic U.S. Representative Anthony Weiner, the estranged husband of Clinton aide Huma Abedin.
Weiner is the target of an FBI investigation into illicit text messages he is alleged to have sent to a 15-year-old girl in North Carolina.
Sources familiar with the matter said FBI agents working on the Weiner investigation saw material on a laptop belonging to Weiner that led them to believe it might be relevant to the investigation of Clinton's email practices.
Trump has highlighted the issue as proof for his argument that Clinton is corrupt and untrustworthy.
"We have one ultimate check on Hillary's corruption and that is the power of the vote," Trump told a rally in Las Vegas on Sunday. "The only way to beat the corruption is to show up and vote by the tens of millions."
Comey, who announced in July that the FBI's long investigation of Clinton's emails during her time as secretary of state was ending without any charges, said in his letter the agency would review the newly surfaced emails to determine their relevance to the investigation of her handling of classified information.
An ABC News/Washington Post poll released on Sunday showed Clinton with a statistically insignificant 1-point national lead on Trump. About a third of likely voters in the poll said they were less likely to back Clinton given Comey's disclosure.
Clinton, who told a Florida rally on Saturday that Comey's letter was "deeply troubling," did not address the issue directly on Sunday but referred vaguely to voters overcoming a "distraction."
"There's a lot of noise and distraction but it really comes down to the kind of future we want and who can get us there," she told a packed gay nightclub in Wilton Manors, Florida, where hundreds of supporters who could not get in lined the streets outside.
"We don't want a president who would appoint Supreme Court justices to overturn marriage equality," she said.