But hours after withering criticism over his comments, Pompeo, a close ally and appointee of Trump's, in a Fox News interview appeared to soften his tone.
"I am very confident that we will have a good transition, that we will make sure that whoever is in office on noon on January 20th has all the tools readily available so we don't skip a beat with the capacity to keep Americans safe," Pompeo said.
Major media and polling outlets called the presidential election for Biden on Saturday but Trump and his allies insist "illegal" ballots may have been cast despite no evidence of mass voter fraud, which is extremely rare in US elections.
Pompeo did not make any comments in either set of remarks to suggest he recognized Biden as the president-elect.
Asked during the Fox interview if he was being "serious" regarding his comments about a "second Trump administration," Pompeo did not say either way but did not repeat the phrase.
He spoke as leaders of other countries, including Washington's close allies Britain and France, already have congratulated Biden. Trump, a Republican, has so far refused to concede and is pursuing lawsuits in several states in a long-shot bid to hold on to power. Republican US lawmakers have defended his right to do so.
"There will be a smooth transition to a second Trump administration," Pompeo earlier told a State Department news conference, drawing a sharp rebuke from Democrats.
Representative Eliot Engel, chairman of the House Foreign Affairs Committee, said the State Department should begin preparing for Biden's transition now. "Secretary Pompeo shouldn’t play along with baseless and dangerous attacks on the legitimacy of last week’s election," he said.
Richard Boucher, a retired diplomat who was the longest-serving State Department spokesman, said Pompeo’s comment about a second Trump administration could be passed off as a joke but also served to protect him from White House criticism.
Pompeo played down suggestions that a delayed transition in the past might have presented a national security risk. "I was part of a transition on the other side ... It didn't take as much time as some might be pretending that it's going to take," he told Fox.
"I'm very confident that all the things that need to be done will be done in an appropriate way, that we will deliver that."
Biden earlier said nothing would stop the transfer of power in the US government.
Asked if Trump's refusal to concede hampers State Department efforts to promote free and fair elections abroad, Pompeo declined to address the specific question but said: "This department cares deeply to make sure that elections around the world are safe and secure and free and fair."In his first official travel after the Nov. 3 election, Pompeo is due to go to France, Turkey, Georgia, Israel, Qatar, United Arab Emirates and Saudi Arabia between Nov. 13-23. The leaders of some of those countries have already congratulated Biden.