Officials said Sudan needed some 7.8 billion dollars (six billion euros), a third of it from the international community, by 2007 for reconstruction after the January 9 peace accords that ended fighting in the country's south.
The United Nations is also seeking 1.5 billion dollars for food and other humanitarian aid throughout Sudan in 2005.
But Zoellick drew a direct link between the supply of assistance and Khartoum's cooperation in halting more than two years of bloodshed in the western Darfur region that Washington has labeled genocide.
"One clear message that I will be delivering publicly as well as in private is that if conditions in Darfur do not improve, neither the United States nor other countries are going to be able to provide the financial support for the North-South accord," Zoellick said.
He said the government of Sudan "has an interest in trying to help deal with the tragedy" in Darfur, where an estimated 300,000 people have died since rebels rose up against Khartoum in February 2003.
"Sudan is at a point of fundamental choice," the number two US diplomat said. "There can be either an upward, positive spiral between these two dimensions of the problem or there can be a negative downward spiral."
Zoellick said Washington hoped to play a major role in Sudan's reconstruction and would announce in Olso it "will be providing between one and two billion (dollars) over about the next year."
He said this included 853 million dollars in committed funds left over from the 2004 fiscal year budget and already appropriated in the 2005 spending plan.
President George W. Bush has sought another 883 millions dollars in a supplementary request for 2005 and in the 2006 budget. "We think we'll get a good portion of that because Congress has been supportive," Zoellick said.
Zoellick said the United States was also making a push to drum up more contributions from the European Union and individual countries but did not lay out any specific figures.
While working to raised badly needed cash for the turbulent African country, the State Department has made it clear that any help should not end up as a windfall for the Khartoum government of President Omar al-Beshir.
"This is not money to support the Sudanese government as it's now constituted," State Department spokesman Richard Boucher told reporters last week.
"Any money that we spend from now on is to implement the north-south accords, which will create a new government in Khartoum, and to help the people of Darfur who are suffering, often at the hands of government-sponsored militia."
Zoellick's mission will follow a flurry of moves at the United Nations to restore order in Darfur and the rest of Sudan.
The UN Security Council last month approved 10,000 UN peacekeepers for Sudan to help shore up the north-south accord. It also voted for sanctions against those committing atrocities in Darfur.
Last month, the council ended weeks of haggling by voting to refer Darfur cases to the International Criminal Court. Washington fiercely opposes the ICC but struck a compromise that gave Americans tighter protection against prosecution.