Citizens for Global Solutions, a US grassroots group promoting global democratic institutions, called the referral - the first by the Security Council to the court, established in 2002, "a historical first for international law".
"It demonstrates that the ICC is the only legitimate international body able to deal with genocide, war crimes and crimes against humanity when states fail to do so," the group said in a statement.
New York-based Human Rights Watch and Amnesty International both called the move historic, but attacked an exemption that would bar the ICC from prosecuting US citizens or those from any other nation in Sudan that was not a party to the court.
Amnesty International's Yvonne Terlingen said the exemption was totally unacceptable"and said it should be excluded from all future Security Council resolutions.
"It creates double standards of justice, contravenes the UN Charter, the Rome Statute and other international law," she said.
Thousands die each month in
Darfur from hunger and violence
Citizens for International Justice said an estimated 20,000 people had died in Darfur during two months of "bickering" about the referral due to US opposition to the ICC.
"The US needs to reassess its policy towards the ICC to ensure that human life is given priority over unfounded political objections," said its vice-president, Heather Hamilton.
Thousands of people in Darfur, in Sudan's west, die each month from violence, hunger and disease, and more than two million have been herded into squalid camps. Most atrocities are blamed on pro-government Arab militia fighting a rebel uprising.
Based in The Hague, the ICC was established in 2002 as the first permanent global criminal court to try individuals accused of genocide, war crimes and major human rights abuses.
A total of 98 countries have ratified the treaty creating the ICC, but Washington opposes the court, fearing US officials would become targets of politically motivated prosecutions.
The United States, which has described killings in Darfur as genocide, abstained from the referral vote after winning the exemptions and insisted it still opposed the ICC, which has yet to issue its first indictment or arrest warrant.