South Korean generals meet Tuesday in Seoul to discuss how to respond to North Korea's reported nuclear test.
(CNN) -- U.N. Security Council members will resume closed-door discussions Tuesday of U.S.-proposed sanctions against North Korea over its claimed nuclear test.
The resumption of talks at the United Nations comes as America's lead negotiator on North Korean issues urged sanctions that are tough enough to show North Korean leader Kim Jong Il that he made a "very, very costly" mistake if a test was indeed carried out.
"He is going to really rue the day that he made this decision," said Assistant Secretary of State Chris Hill Monday in an interview with CNN.
The U.S. proposals include cargo inspections and an embargo on goods that could be used in Pyongyang's missile and nuclear programs.
North Korea's announcement triggered widespread international condemnation and set off alarm bells in neighboring capitals. (World reaction)
On Tuesday, South Korean President Roh Moo-hyun said his country would reconsider its policy of engagement with the North, according to a report from the Reuters news service.
Australia said it would impose various measures on North Korea, including curtailing visas and supporting any U.N. sanctions. Japan said it was weighing stricter economic sanctions against its isolated neighbor.
Even close North Korea ally China signaled its dismay by telling a visiting South Korean envoy that Beijing appears ready to drop opposition to tough U.N. sanctions.
"China seems to have a different position than it had before on a Chapter 7 resolution," South Korea's nuclear envoy Chun Young-woo told The Associated Press.
However, a North Korean official said Pyongyang would return to international arms talks and abandon its atomic program if the U.S. takes "corresponding measures," South Korea's Yonhap news agency reported Tuesday.
On Monday, after speaking with the leaders of China, South Korea, Russia and Japan, U.S. President George W. Bush condemned what he termed a "provocative act" -- and bluntly warned North Korea against trying to export its nuclear know-how. (Full story)
The president said he assured the leaders of Japan and South Korea, both close U.S. allies, that the United States "will meet the full range of our deterrent and security commitments" to them. However, Bush insisted the United States "remains committed to diplomacy" to settle the dispute. (Watch Bush on why North Korea's move poses a threat -- 2:34 
)
Analysis shows small explosion
Meanwhile, scientific analysis of an explosion, which North Korea said was a successful nuclear test, raised questions about the claim. (Watch why scientists are still assessing information on the test -- 2:16)
The apparent nuclear test was conducted at 10:36 a.m. Monday in Hwaderi near Kilju city, South Korea's Yonhap news agency reported, citing defense officials. (Map)
U.S., French and South Korean experts estimated that the power of the explosion, about 240 miles northeast of Pyongyang, was equivalent to about 500 metric tons of TNT, which a senior U.S. intelligence community official said was unusually small for a nuclear blast.
By comparison, nuclear tests in 1998 by India and Pakistan were about 24 to 50 times as powerful, according to the Federation of American Scientists. (Nuclear nations)
Also, the small size of Monday's explosion may make it difficult for geological sensors to pick up radioactive emissions that would effectively confirm a nuclear test -- raising the possibility that the international community may never know for sure whether North Korea actually has a working nuclear bomb.
Despite the ambiguity, Hill said U.S. officials "have to work under the assumption that North Korea did what it said it was doing" and push for a tough sanctions resolution at the U.N. Security Council.
"We're just not going to accept that North Korea, with its starving population, is going to be able to join the nuclear club," Hill said. "We're going to work very hard to make sure North Korea understands the cost of this." (Time.com: What can the U.S. do
?)
North Korea recently has test-fired seven missiles, including a long-range ballistic missile in July, but it's unknown whether Pyongyang possesses the high-technology expertise to construct a nuclear device small enough for a missile delivery system. (Missile range map)
U.S. Security Council debate sanctions
The Security Council Monday unanimously condemned North Korea's announcement, and diplomats began hashing out the details of a sanctions resolution.
A draft proposed by the United States calls for an international embargo on any goods or materials that could be used in North Korea's missile and nuclear programs, as well as inspections of cargo going into and out of the country. (Watch why experts worry about other countries in region -- 2:40 )
It would also prohibit financial transactions that might support missile activities, freeze assets related to North Korea's weapons program, impose a ban on luxury goods and take steps to prevent counterfeiting by the Pyongyang regime.
The sanctions would be approved under Chapter 7 of the U.N. Charter, which would make them binding on all U.N. members.
In addition, Japan has proposed denying North Korean ships and planes permission to travel outside the country, banning imports of North Korean products and a prohibiting international travel by high-level North Korean officials.
While senior U.S. officials said there appeared to be "substantial" support for "strong sanctions," it remains unclear whether Russia and China -- which hold veto power on the Security Council and have voiced opposition to U.N. sanctions on Iran for its nuclear program -- would go along with a tough punishment for North Korea.
The U.S. ambassador to the United Nations, John Bolton, said the early reaction by Russia and China to the strong U.S. approach was "positive."
"I think they were taken by surprise by this test," Bolton said. "I think they realize how unacceptable this is."
China role seen as critical
Hill said the U.S. view is that China -- as North Korea's neighbor and long-time patron -- will be key to getting a meaningful sanctions regime passed, and he expressed optimism that could happen, given the strongly worded rebuke the Chinese government offered after North Korea's announcement.
"China is clearly, clearly upset," Hill said. "The Chinese have indicated they're going to work with us in New York, and we'll see what we get. But I think we can get something that will be far more than just some sort of angry letter. I can assure you of that."
However, Hill stressed that the United States would be working with the international community on a response and would not act unilaterally.
North Korea's U.N. ambassador, Pak Kil-yon, said Monday that the council should "congratulate" his country's scientists and researchers on their achievement, instead of issuing what he called "notorious, useless and reckless resolutions."
Pak said the test was "very, very successful" and will contribute "to the maintenance and guarantee of peace and security in the (Korean) peninsula and the region." (Text of North Korea statement)
CNN's Sohn Jie-Ae, Elise Labott, Jamie McIntyre, Liz Neisloss and Barbara contributed to this report