"If you really care for the country, at the very least, exhaust these legal challenges as quickly as is absolutely possible, ideally by early next week," Petraeus said on CNBC's "Squawk Box." "Then you can get on with this."
While NBC News and other media organizations have projected Democrat Joe Biden as the winner of last week's the presidential contest, Trump has refused to concede. His campaign has launched a flurry of lawsuits related to the voting process or the vote counting. However, there is no evidence of widespread voter fraud, despite Trump's baseless insistence that his loss is due to "illegal votes."
Biden, vice president under former President Barack Obama, has nonetheless launched his transition team, announcing various advisory groups and delivering presidential-like speeches on health care and the coronavirus pandemic in recent days. On Tuesday, Biden called Trump's refusal to concede "an embarrassment, quite frankly."
Petraeus, who previously served as director of the CIA under Obama, said he believes the Trump administration should at least allow important aspects of the transition to a new president to happen concurrently with any legal proceedings.
"My hope would be, obviously, that whatever legal challenges are raised will be resolved very expeditiously," he said. "I don't understand why in the meantime, actually, you still can't get on with a transition in terms of the time-consuming tasks," Petraeus added, such as background checks for people who will need high-level security clearances.
White House spokesman Judd Deere said in an email to CNBC that the Trump administration "is following all statutory requirements" related to a transition of power.
Secretary of State Mike Pompeo on Tuesday predicted a smooth transition to a second Trump term. This week, Senate Majority Leader Mitch McConnell and some other Republicans rallied behind Trump's right to fight the election results in the courts.
In a statement, Trump campaign spokesman Tim Murtaugh also defended the president's legal maneuvers. "Every American deserves to be able to trust that our elections are free, fair, safe, and secure. The President owes that to everyone who voted for him, and to those who voted for Joe Biden as well," Murtaugh said in an email. "This is not just about this election, but every election in the future."
"I'm nonpartisan. I don't favor either party, but I do favor the country," said Petraeus, chairman of KKR Global Institute. "I do believe that we should enable the incoming team to have as smooth of a transition as is absolutely possible for the good of the country."
Inauguration Day is set for Jan. 20.
Petraeus, a retired four-star Army general who oversaw years of operations in Afghanistan and Iraq, said he learned lessons about transitioning to new roles from a mentor, Ret. Gen. Jack Keane.
"He used to tell the battalion and brigade commanders, 'If you really love your unit, if you really care for it, you will suppress your ego, you'll let your successor into the organization before you even leave, before the change of command,'" he said.
Petraeus resigned as CIA chief in 2012, under fire for sharing classified information with his biographer, with whom he was having an extramarital affair. He later pleaded guilty to mishandling classified information and was fined and put on probation.