Story Highlights• NEW: U.S.: Next move is up to Pyongyang
• NEW: Bolton, Rice expect China to comply with resolution despite inspection issue
• World body punishes North Korea for claimed nuclear weapons test
• NK ambassador "totally rejects" resolution, and walks out of chamber
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NEW YORK (CNN) -- The United States is maintaining diplomatic pressure on China to help enforce U.N. sanctions on North Korea for its claimed nuclear test.
The chief U.S. diplomat, Condoleezza Rice, leaves Tuesday for a trip throughout Asia in a bid to maintain a unified world diplomatic front against North Korea, which announced last week that it had successfully carried out a nuclear test.
Over the weekend China joined in the security council's 15-0 approval of a U.S.-drafted package of financial and weapons sanctions against North Korea.
Beijing has made clear, however, that it would not conduct searches of cargo going to and from North Korea.
One section of the resolution calls for cargo going in and out of North Korea to be searched for prohibited items that could be used in weapons of mass destruction, including nuclear weapons.
In a bid to ease concerns from China, U.S. Secretary of State Rice said Washington wanted to implement the sanctions in a way that avoided "open conflict" with North Korea, according to a report from The Associated Press.
U.S. ambassador to the United Nations John Bolton said on Sunday that he expected China to comply with the resolution, in spite of statements from China's U.N. ambassador that suggested the opposite.
"The guts of the resolution is to prohibit trade in weapons of mass destruction-related materials and high-end conventional military equipment, and I'm sure, sure that China is going to abide by the very resolution that it voted for," Bolton told CNN's "Late Edition with Wolf Blitzer."
"How it accomplishes that I'm sure we'll have discussions about, but let's be clear: They voted in favor of the resolution that provides for inspection regime."
"China signed on to this resolution, it voted for this resolution ... so I am quite certain that it is going to live up to its responsibilities," she told FOX News Sunday.
"I'm quite certain that China has no interest in seeing the proliferation of dangerous materials from North Korea," Rice said.
Resolution 1718, which the Security Council passed on Saturday by a 15-0 vote, forbids trade between U.N. member states and North Korea in high-end military equipment and material that may be used for nuclear and other weapons of mass destruction. (Full story)
The resolution requires that Pyongyang not conduct further nuclear tests or launch ballistic missiles and demands that the country abandon all programs to develop weapons of mass destruction.
It also bans trade in luxury goods, and requires member states to freeze the assets of North Korean entities and individuals.
Asked about the impact of banning the import of luxury goods to North Korea, Rice said the action has probably at least caught the attention of "a regime that very much likes luxury for itself while it starves its own people."
Rice emphasized the statement made by the unanimous U.S. Security Council vote.
"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," Rice said.
The resolution also calls on member states to "refrain from any actions that might aggravate tension and to facilitate the early resumption of the six-party talks," the discussions that Pyongyang dropped out of last year that also included the United States, China, Japan, Russia and South Korea. (Resolution text)
Bolton said that while Resolution 1718 only calls for sanctions, it does not preclude another resolution down the road that might call for something stronger. For the time being, though, diplomacy is the method being used.
"I think the president has made it clear on any number of occasions that we want to solve the problem ... through peaceful diplomatic means," he said.
But Bolton stressed that the next move is up to North Korea,.
"The ball is really in North Korea's court to see in what direction we go here," he said.
The language of the text also says that depending on North Korean compliance, the sanctions could be increased, modified, suspended or lifted, Bolton explained.
After the resolution was passed in the Security Council, North Korean representative Pak Gil Yon said that his country "totally rejects the unjustifiable resolution" and vowed that if the United States increases "pressure upon the Democratic Peoples of the Republic of Korea persistently, the DPRK will continue to take physical countermeasures, considering it as a declaration of war."
After Pak spoke, he left the chamber. (Watch Pak accuse council of being "gangster-like" -- 5:15)
Bolton said Sunday he hopes the representative's comments "will not reflect the considered judgment in Pyongyang after they consider the terms of the resolution."
Japanese Prime Minister Shinzo Abe said Sunday his country was considering additional measures against North Korea. (Full story)
Japan has already taken a number of steps, including closing its ports to North Korean ships, banning trade with the North and barring entry to North Korean citizens, except those already living in Japan.
Source: John Bolton, U.S. ambassador to the United Nations
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