Signing comes amid moves by Pyongyang to dismantle its nuclear programme.
He said North Korea must first agree to international terms for verifying efforts to dismantle its bomb-making plutonium nuclear programme as detailed in the declaration delivered in June.
He also said that it was premature to drop Pyongyang from his “axis of evil”, adding that it had “a lot to do” before removal from the US blacklist.
“They got to show a verification regime that we can trust,” he said.
Speaking at a joint news conference in Seoul with Lee on Wednesday, Bush also urged China to allow free expression and worship.
The president, who will be attending the opening ceremony of the Olympic games in Beijing on Friday, said Chinese leaders “ought to welcome people being able to express their minds, and to the extent that people aren’t able to do that and people aren’t able to worship freely, is a mistake”.
North Korea expects the US to remove it from the terrorism blacklist earliest by next weekend, and subsequently relax some economic sanctions, as part of a six-party denuclearisation pact.
But Bush said he still had concerns about the North.
“I told the president [Lee] I’m concerned about North Korea’s human rights record. I’m concerned about uranium enrichment activities as well as nuclear testing and proliferation and ballistic missile programmes,” he said.
“The best way to approach and answer the concerns is strong verification measures. That’s where we are in the six-party talks.”
The US also accuses the North of operating a secret highly-enriched uranium weapons programme, a charge it denies.
“The North Korean leader has yet to fully verify … a highly enriched uranium programme and there are still more steps to be done on the plutonium programme,” Bush said.
“In order to get off the ‘axis of evil’ list, then the North Korean leader is going to have to make certain decisions.”