They appeared to back away from a reported proposal under which, Washington would list its concerns about the North's activities, which Pyongyang would then acknowledge.
Some US conservatives have criticised that idea as "giving in" to North Korea.
"You know, there's all kinds of rumours about what is happening and what's not happening," Bush said at a joint news conference with Lee.
"Obviously I'm not going to accept a deal that doesn't advance the interests of the region."
North Korea, which tested a nuclear device in 2006, failed to meet a December 31 deadline to reveal its nuclear programme, a deal struck with the US, China, South Korea, Japan and Russia.
"So we'll wait and see what he [Kim Jong-il, North Korean leader] says, and then we'll make a decision about our obligations, depending upon whether or not we're convinced that there is a solid and full declaration," Bush said.
If Pyongyang makes the statement, the US is expected to ease some sanctions imposed under the US "state sponsors of terrorism" list and the US Trading With the Enemy Act.
For his part, Lee said that there should be no let-up in pressure on Pyongyang to live up to its agreement.
"The verification process has not begun. We are still waiting for North Korea to declare their full programme. They should not get away with this temporary measure," he said.
Need for trust
"I think it is inappropriate and unconstructive for us to have too many doubts before the process begins. We should have trust in the process, and I will watch this process and co-operate fully," Lee said.
Despite his tough stance, he said he was open to a summit with Kim if the talks would generate results.
"I will agree to it when the need is real and I already said publicly that I am willing to meet with him not just once, but many times, but if the meeting will yield substantial and real results," Lee said.
He proposed on Thursday that North and South Korea, technically still in a state of war since 1950, establish permanent liaison offices in each other's capital.