Bush would not commit to handing over Saddam by the 30 June transfer of power, as asserted by interim Iraqi Prime Minister Iyad Allawi, but Bush did not rule it out.
He said the United States would not allow "lax security" to jeopardise plans for Saddam to be tried by a special tribunal.
"He is a killer. He is a thug. He needs to be brought to trial," Bush said on Tuesday at a Rose Garden news conference with Afghan President Hamid Karzai.
"We want to make sure that he [Saddam] doesn't come back to power. And so therefore, it's a legitimate question to ask of the interim government: 'How are you going to make sure he stays in jail?' And that's the question I'm asking. And when we get the right answer, which I'm confident we will - we'll work with them to do so - then we'll all be satisfied," Bush said.
"I'm confident that when it is all said and done, he will stay in jail. I just want to be assured," he added.
Allawi said on Monday that Saddam and other prisoners would be given to the new Iraqi government within two weeks to prepare for trial.
But in a potential rift, Bush and his spokesman, Scott McClellan, were noncommittal about the timing. "We're going to turn him over at the appropriate time ... We're talking to them about those issues, and about the process for turning them over," McClellan said.
Bush also stood by Vice-President Dick Cheney, who claimed on Monday that Saddam Hussein had "long-established ties" to al-Qaida. That contention has long been challenged by some lawmakers and analysts.
"I'm confident that when it is all said and done, he will stay in jail. I just want to be assured"
Bush cited the presence in Iraq of Islamist fighter Abu Musab al-Zarqawi as "the best evidence of [a] connection to al-Qaida affiliates and al-Qaida".
The US is under pressure to quickly bring charges against the former Iraqi president.
The International Committee of the Red Cross said prisoners of war and all other detainees in Iraq should be entitled to due legal process after the 30 June handover.
US occupation troops captured Saddam Hussein in December near his home town of Tikrit and he has been in US custody since, held as a prisoner of war at an unknown location.