Attorney General Eric Holder decided to try KSM in federal court in New York, but a number of politicians, from New York and elsewhere, have since spoken out against the plan.
Appearing on ABC's "This Week," Cheney said he had similarly disagreed when the Bush administration tried shoe bomber Richard Reid in a civilian court, saying he should have been declared an enemy combatant and held in military custody. [Reid was convicted of trying to destroy an airliner in December 2001.]
"We could have put him into military custody," Cheney said.
Biden, however, said civilian trials have been more effective in keeping accused terrorists in prison.
"We have no doubt the best, most effective legal way to get his guy behind bars for the longest time and get the most information with the most certainty is in an Article Three court," he said, referring to the federal system.
Biden told moderator Bob Schieffer that the only reason the president would consider a military tribunal in the case of Mohammed is if Congress were to limit funding a federal case.
The president, however, is now waiting for a recommendation from Holder as to whether there are other options, Biden said.
In the meantime, Biden said the administration is working with lawmakers like Republican Sen. Lindsey Graham to make sure the military tribunal system would stand up to constitutional scrutiny.
He also said that the perception that if found guilty KSM is more likely to receive a greater punishment before a military tribunal than in a civilian court is incorrect.
"There have been three people tried and convicted by the last administration in military courts. Two are walking the street right now," Biden said. "There have been over 300 tried in federal courts by the last administration and by us. They're all in jail now."