Speaking on the latest leg of a regional tour aimed at restarting stalled talks, Hill said the reclusive communist state had to show "full transparency" for the process to move forward.
His remarks came after talks here with incoming South Korean president Lee Myung-Bak, who formally takes office on February 25 and has indicated he will take a tougher line on the North than his predecessor.
The Pyongyang regime missed a key December 31 deadline to disable its main nuclear facilities and give a full declaration of its atomic programmes.
That was supposed to be the second phase of a landmark February 2007 deal, after phase one -- the simple shutting down of its main Yongbyon nuclear plant -- was carried out in July.
"It will be very desirable if we could complete the phase two even before this government comes in," Hill said, referring to Lee's administration.
"By the time this government does come in, the end of February, we will be focusing on that last phase."
The proposed final phase is for the North to actually dismantle its plants and hand over all nuclear materials.
In return for compliance, North Korea would get up to one million tonnes of fuel or equivalent economic aid as well as diplomatic concessions, including full relations with the United States and Japan and a formal peace treaty.
Hill, speaking at Incheon airport, west of Seoul, before flying to Beijing, said a transparent declaration was key to moving the process forward.
After landing in Beijing, the US envoy said he would be meeting his Chinese counterpart Wu Dawei later in the day on fixing a date for resuming six-party talks.
No date has been set yet for talks to push forward the deal agreed by the two Koreas, China, the United States, Japan and Russia in February 2007.
Hill, who started his regional tour earlier this week in Tokyo, will travel Friday to Moscow.
"I think it really has to do with transparency," Hill said at Incheon.
"As we are going forward here, we need to have an understanding of how we go forward. We can go forward with full transparency.
"We can't have a situation where we pretend programmes didn't exist for we both know that they existed."
Nevertheless, Hill was positive that progress would be made.
"I want to emphasize that throughout the six-party process, we had these bumps in the road, we had these missed deadlines, but ultimately we had been able to continue to make progress," he said.
Hill, who earlier Thursday met Lee in Seoul, stressed the US-South Korean alliance would be very important in tackling a raft of issues including North Korea's disarmament.
"The ROK (South Korea) has been a very strong participant in the six-party process," he said. "I am sure that the engagement of the ROK in the six-party process will continue as it has been."
Lee, whose conservative government is a change of tone in South Korea after a decade of liberal rule, insists the North must first remove all its nuclear weapons before getting meaningful aid and economic assistance from Seoul.
Hill said he had briefed Lee on the nuclear negotiations, "emphasizing that in order to make what we have done successful, we need to finish, we need to go and we need to continue this third phase."
He also said he had delivered a message from US President George W. Bush, who wanted Lee to visit Washington sooon after his February 25 inauguration.
He indicated Secretary of State Condoleezza Rice may visit Seoul to attend that ceremony, according to officials in the transition team here.