WASHINGTON — The U.S. called on China on Wednesday to use its political clout to rein in North Korea as American officials confronted the limits of their influence over one of the world’s most unpredictable, and least understood, nuclear powers.

Adm. Mike Mullen, the chairman of the Joint Chiefs of Staff, said during an appearance on ABC’s “”The View,”” that China’s role was “”critical”” to keeping North Korea from undertaking provocative acts such as Tuesday’s shelling of a South Korean island, which left four people dead, including two civilians.

“”The one country that has influence in Pyongyang is China,”” Mullen said, referring to North Korea’s capital. “”Their leadership is absolutely critical.””

That view was echoed by State Department spokesman Phillip J. Crowley, who called China’s influence “”pivotal to moving North Korea in a fundamentally different direction.””

“”We would hope and expect that China will use that influence first to reduce tensions that have arisen as a result of North Korean provocations, and then secondly, continue to encourage North Korea to take affirmative steps to denuclearize,”” Crowley said.

But few in Washington expect China to take any major steps, and Chinese news accounts steadfastly avoided any criticism of the north’s actions. Xinhua, the official Chinese news agency, quoted a Chinese official as urging both North and South Korea to “”do things conducive to peace.””

“”We hope related parties do things conducive to peace and stability in the Korean Peninsula,”” the agency quoted a Chinese foreign ministry spokesman, Hong Lei, as saying.

Meanwhile, U.S. officials and defense experts said the U.S. response is complicated by the lack of knowledge of what precisely drives the North Koreans, who earlier this month also unveiled to visiting American scientists new uranium refining capabilities that will allow them to add to the country’s stockpile of perhaps as many as a dozen nuclear weapons.

No new military confrontations were reported Wednesday, but South Korea raised the death toll from the shelling to four, saying that rescuers had found two dead civilians on Yeonpyeong Island, home to about 600 families. On Tuesday, the South Koreans reported that the shelling had killed two marines and injured 16 other soldiers.

Mullen said he thinks the North Korean shelling may have its roots in an effort by North Korean leader Kim Jong Il to shore up support among the military for his plan to have his son, Kim Jon Un, succeed him. The younger Kim was promoted to general earlier this year, but is reported to have little backing within the military.

“”We think this is tied to the succession of his young 27-year-old son,”” Mullen said.

Others, however, said North Korea’s actions may be intended to gain the attention of the international community and persuade the U.S. to resume six-party talks, which were designed to peacefully resolve North Korea’s resumption of its nuclear program in 2003.

The North Koreans may hope resumed talks will lead to “”substantial aid,”” said Victor Cha, who holds the Korea chair at the Washington-based Center for Strategic and International Studies. In the past, Cha said, North Korean provocations have elicited public rebuke but yielded private food and economic assistance from the South.

Whatever the motive, Washington has few options to counter North Korean attacks.

The aircraft carrier USS George Washington and its retinue of support ships departed Japan on Tuesday to participate in joint naval exercises with the South Koreans, a step that was announced late Tuesday after President Barack Obama to his South Korean counterpart, President Lee Myung-bak.

But Pentagon spokesman Marine Col. David Lapan said the exercise in the Yellow Sea from Nov. 28 to Dec. 1 had been planned previously and that the ships actually left Japan before Obama and Lee spoke.

The U.S. military has conducted at least three joint exercises with South Korea this year. The George Washington last participated in a joint exercise with South Korea in October 2009.

U.S. Forces Korea, in an official announcement, called the maneuvers “”defensive in nature”” and said they demonstrated “”the strength”” of the South Korea-U.S. alliance and “”our commitment to regional stability to deterrence.””

The U.S. troop presence in South Korea has been dwindling for years, and now stands at 28,000. North Korea’s army is estimated to number 1.1 million.

But Cha said the presence of the American troops serves as a deterrent to a major war, which North Korea fears would spark massive American retaliation. The troops’ presence has been less successful in stopping North Korea from developing nuclear weapons or undertaking attacks such as Tuesday’s artillery barrage or the March torpedo strike on a South Korean ship that killed 46 sailors.

The U.S. presence “”assures against major war. But it isn’t something you can turn on and off for smaller problems. It isn’t the golden rule,”” Cha said.

At the same time, China’s influence has grown. Cha said that reflects a strong Chinese economy, not a weaker U.S. military presence.

“”The metric for American decline in Asia is not its military presence but our financial catastrophe,”” Cha said.

Whether China will use that influence is an open question.

“”We believe fundamentally that China and the United States share the same interest,”” the State Department’s Crowley said Wednesday. “”Where we will continue to talk to China is what is the best way to put ourselves in the strongest possible position to see North Korea make the right choices and avoid the wrong choices. There’s no guarantee here.””