His answer: the botched raid to rescue American hostages in Iran.
"I wish I'd sent one more helicopter to get the hostages and we would have rescued them and I would have been re-elected," Carter said.
His response elicited laughter from the audience, but his comment pointed to the enduring significance of the seizure of 66 Americans from the U.S. Embassy in Tehran by Iranian revolutionaries in 1979. They came as the U.S. has been engaged in raucous debate over American policy toward Iran and the wisdom of a deal the White House recently made with Tehran to curb its nuclear program.
The mission authorized by Carter, Operation Eagle Claw, came to a grisly end when a helicopter crashed into a C-130 in the Iranian desert, killing all eight servicemen on board. The hostages remained in Iranian hands until 20 minutes after Ronald Reagan was sworn in as president, and the national attention to the crisis was widely seen as a leading reason for Carter's loss to the California governor.
The frozen relations between the U.S. and Iran have continued to this day, but there has for the first time been high-level one-on-one contacts between the two governments during the nuclear negotiations.
Washington is now embroiled in a debate over the historic deal, with Congress set to vote on whether to accept it in mid-September. Critics have charged the administration with cozying up to Iran and seeking to form a new alliance with the Islamic Republic, which the White House strongly denies.
Carter reflected on his handling of the Iran hostage crisis and the ongoing conflict in the Middle East Thursday after announcing he will undergo treatment for melanoma cancer.
The 39th president was asked what he'd do differently if he could redo his time in the White House.
He followed his answer about sending another helicopter on the hostage rescue mission with the reflection that staying at 1600 Pennsylvania Ave. might have interfered with his later humanitarian work.
"That may have interfered with the foundation of the Carter Center, and if I had to choose between four more years, I think I would choose the Carter Center," he said.
Carter held the press conference at the center, a human rights non-profit that works on international issues.
Carter also said reducing conflict in the Middle East has been part of his life's work.
"In international affairs, peace for Israel and its neighbors has been a top priority of mine for the last 30 years," he told reporters. "Right now, I think the prospects are more dismal than anytime I remember in the last 50 years. This whole process is practically dormant."
Carter has been a critic of the Obama administration's handling of the the Israeli-Palestinian negotiations and other aspects of its foreign policy.
"The government of Israel has no desire for a two-state solution ... and the United States has practically no influence compared to past years in either Israel or Palestine, so I feel very discouraged about it," he said.
Carter said Secretary of State John Kerry is one of the various dignitaries who called him after the state of his health was made public. The former president previously said Kerry was "having a difficult time operating pretty much on his own" regarding Middle East negotiations.
It was "the first time he called me in a long time," Carter said Thursday to laughter.