Mr Hill will arrive in Japan on Monday to meet his Japanese counterpart, Kenichiro Sasae, before continuing to South Korea.
He is then expected to join US Secretary of State Condoleezza Rice who will arrive in Soeul on Tuesday.
Mr Hill is the chief US delegate in stalled six-nation talks on ending North Korea's nuclear drive.
The pair will have a tough job ahead of them trying to bolster the resolve of reluctant partners to clamp a cordon around North Korea.
Dr Rice is visiting Japan, China and South Korea to thrash out how to enact the new UN Security Council resolution.
The resolution was approved at the weekend and imposes sanctions on North Korea over its announced October 9 test of a nuclear bomb.
China joined the 14 other members of the UN Security Council on Saturday in voting for unprecedented punitive action to force North Korea to give up its nuclear arms and return to six-nation talks on ending the state's isolation.
The central measure of the sanctions, pushed hard by the United States and Japan and accepted only reluctantly and in a watered-down form by China and Russia, aims to prevent the cash-strapped North Korean regime from spreading its nuclear know-how.
The resolution calls on UN member states to take "cooperative action
including through inspection of cargo to and from (North Korea), as necessary, ... to prevent illicit trafficking in nuclear, chemical or biological weapons, their means of delivery and related materials."
It does not, however, provide additional authority for such inspections or require China to police its long land border with North Korea.
The two carried out some 1.7 billion dollars in trade over the past year, making China far and away Pyongyang's biggest economic partner.
Barely an hour after the UN vote Saturday, Beijing reaffirmed it did not intend to carry out cargo inspections for fear of "negative consequences".
Dr Rice played down the remarks, insisting on the importance of Beijing's vote in favor of the most far-reaching sanctions ever imposed on North Korea.
"You cannot underestimate how big a blow it is to North Korea to have all of the neighbors now, including what has been its strongest supporter, China, fully united behind sanctions against its nuclear program," she said.
But she admitted a tough road lay ahead to actually enact the sanctions.
"It will take some work to talk about the implementation of the resolution, that's part of what I will do when I go out to the region on Tuesday," Dr Rice said in a television interview on Sunday.
Dr Rice said a key element of her talks would include "very serious discussion of how to use this interdiction provision", which she called a "very powerful tool" against North Korea.
But she also indicated Washington was prepared to act even in the face of opposition by China and Russia.
"We are prepared to do what we need to do to make certain that North Korea is not exporting dangerous proliferation materials," she said.
John Bolton, the hawkish US ambassador to the United Nations, said
Washington had the means to act outside the UN framework through an informal alliance created by US President George W. Bush in 2003 called the Proliferation Security Initiative (PSI).
"The intention that we have ... will be to continue to carry out the
inspections that we deem necessary," he said.
The initiative, which Washington says has the support of some 70
governments, tracks and intercepts ships and aircraft suspected of carrying illicit weapons-related cargo.
But of the four other nations most closely involved in confronting North Korea -- China, Japan, Russia and South Korea -- only Japan has joined the PSI and Japanese officials have said they do not want to risk involvement in interdiction operations around North Korea.
Kim Geun-Tae, chairman of South Korea's ruling Uri Party, also said over the weekend that Seoul should not at this point take part in searches of North Korean cargo for fear of sparking an armed clash.
Mr Bolton said on Sunday that the "overwhelming predominance" of search and seizure operations against North Korea would take place when suspect cargo reached foreign shores.
But he would not rule out risky high-seas interdiction efforts and a senior US official said Dr Rice would be pressing her interlocutors over participation in the security initiative during this week's talks.