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In January, South Sudan cut off the flow of oil to Sudanese refineries following a dispute with the government in Khartoum. The move crippled the economies of both nations, which rely on oil for a significant portion of their income.

Sen. John F. Kerry, Massachusetts Democrat and chairman of the Senate Foreign Relations Committee, said the South Sudanese government’s decision to shut off the oil may have been justified but also was “self-defeating.”

Sen. Richard G. Lugar of Indiana, the senior Republican on the committee, noted that the 2005 peace agreement between Sudan and the southern rebels held out the promise that both sides would share the petroleum wealth.

“Instead, however, oil exports have stopped, putting an upward pressure on oil prices globally,” he added.

The U.S. imports no oil from Sudan. However, the absence of Sudanese crude from the world market puts pressure on oil prices.

“What happens in Sudan matters very much to us now, economically,” Mr. Clooney said.

Mr. Lyman said that even if a deal on oil is reached soon, it could take up to four months before oil revenues start flowing again.

“[T]hat is worrisome,” he added.

Southern rebels in the Nuba Mountains have joined forces with two rebel groups in Darfur.

The Sudanese government has blocked humanitarian aid from reaching areas controlled by the rebels in Blue Nile and Southern Kordofan.

Nancy Lindborg, an assistant administrator at the U.S. Agency for International Development, said up to 250,000 people in these two states will be “one step short of famine by the end of April” if the violence does not stop.

Mr. Clooney suggested that the United States put pressure on Khartoum by working with China, which imports a majority of Sudanese oil and is most affected by the shutdown. He also suggested freezing the assets of Sudanese officials wanted for war crimes.

Mr. Clooney has used his star power to put the international spotlight on Sudan. However, he acknowledged a “misery fatigue” among an audience constantly exposed to news of conflict.

On Thursday, he will brief President Obama and Secretary of State Hillary Rodham Clinton on his trip to Sudan.