Bush, speaking at a news conference with South Korean President Lee Myung-bak, said North Korea must first agree to international terms for verifying its dismantlement efforts.
"I don't know whether or not they're going to give up their weapons," Bush said. "I really don't know. I don't think either of us knows."
Lee called North Korea "a very difficult opponent."
But, he added: "I will be patient and I will be consistent. I have faith we will be able to move to the verification process, then to the next step."
Bush once branded North Korea as part of an "axis of evil," along with prewar Iraq and Iran, and spoke derisively of North Korean leader Kim Jong Il. The president said it is still "to be determined" whether Pyongyang can come off, and ticked off some of what is left to do.
The North, which exploded a nuclear device in 2006, is believed by experts to have produced enough weapons-grade plutonium to make as many as 10 nuclear bombs, and the U.S. has accused Pyongyang of running a second weapons program based on uranium. Actual destruction of weapons - the ultimate goal of six-party talks with North Korea - is months away at the least.
"The human rights abuses inside the country still exist and persist. The North Korea leader has yet to fully verify the extent to which he has had a highly enriched uranium program. There's still more steps to be done on the plutonium program," Bush said.
"In order to get off the list, the axis of evil list, the North Korean leader is going to have to make certain decisions."
Still, he said he hoped to see all that come to pass.
"My hope is that the axis of evil list no longer exists. That's my hope for the sake of peace. That's my hope for the sake of our children," Bush said.
Bush opened a three-nation Asian trip here that will take him to Thailand, and then on to China at the end of the week for the Olympic Games in Beijing. With widespread talk of China's repression of freedoms for its citizens leading into its hosting of the games, Bush pointedly called such policies by the communist regime "a mistake."
He said he tells Chinese leaders this every time he has met with him over the nearly eight years of his presidency.
"You should not fear religious people in your societies," Bush said, describing the message he delivers, then and now. "As a matter of fact, religious people will make your society a better place. You ought to welcome people being able to express their minds. To the extent that people aren't able to do that, people aren't able to worship freely is - you know - I think is a mistake."
Bush's South Korean visit provided a contrast, as he was greeted by dueling demonstrations by prayerful, flag-waving supporters of the U.S. president and rowdy protesters doused by police water cannons. This divide reflected the U.S.-South Korean relationship, which has endured volatile moments this year.
"I enjoy coming to a free society where people are able to express their opinions - and your country is a free society," Bush told Lee earlier when they first met at the presidential mansion.
Lee, a pro-American leader who took office in February, has seen his approval ratings tumble after lifting a ban on U.S. beef imports despite public fears about its safety. The public outcry prompted street protests that drew attention worldwide earlier this year.
During their news conference, Lee was asked whether Bush had asked Seoul to send more troops to Afghanistan. The South Korean president said: "There was no such discussion." Bush said he asked Lee "to consider as much noncombat help as possible."
South Korea ended a five-year deployment of army medics and engineers to Afghanistan last year. It had planned the withdrawal, but reconfirmed that pledge to the Taliban to win the freedom of 21 kidnapped South Korean civilians in July 2007 after the insurgents killed two hostages.
