But they stopped short of fixing a deadline for Khartoum to honour pledges to disarm the so-called Janjaweed militias, accused of a brutal campaign that has killed more than 10,000 and forced one million to flee their homes.
"The Sudanese government doesn't have forever," Annan told reporters at UN headquarters in New York on Wednesday.
"Serious crimes have been committed and there has been gross and systematic abuse of human rights. We, the international community, must intensify our efforts to protect the innocent in Darfur," he said.
Annan said he did not want to set an "artificial deadline" for further international action if it was determined that Sudan had not kept its commitment to ease the crisis. He said any such date was "a judgment call."
The US said it would present a revised draft Security Council resolution on Thursday amid mounting international concern over what UN officials call the worst humanitarian catastrophe in the world.
"It's the responsibility of the government of Sudan. They've created this monster."
US envoy to UN
"It's the responsibility of the government of Sudan," US ambassador John Danforth said. "They've created this monster."
US Secretary of State Colin Powell will meet Annan on Thursday to discuss Darfur, State Department spokesman Richard Boucher said in Washington. Powell and Annan travelled to Sudan earlier this month.
"They both think it's time to get together now to look very carefully at the situation, as the Security Council is currently doing, and to see what more they can do to try to get progress on the ground," Boucher said.
On his visit earlier this month, Annan got Khartoum to agree to a series of steps, including immediately disarming the militias it is accused of supporting, and improving access for aid workers in the troubled region.
"Access has opened up but there has been little progress on human rights," Annan said. "There are continuing reports of attacks by the Janjaweed."
Many Sudanese children are now
orphans owing to the fighting
A revolt against the government in Khartoum broke out in February 2003.
In retaliation, the pro-government Janjaweed militias have carried out what UN officials and rights groups have said is a brutal campaign of ethnic cleansing.
A first version of the US resolution, which would have slapped sanctions on the Janjaweed but did not call for similar steps against the government, did not garner much support from council members.
But British ambassador Emyr Jones Parry said he thought the 15-nation council could now "quite speedily" agree on an amended resolution that would send a "very firm" message to Khartoum
"The primary purpose of the Security Council now is to ensure effective action on the ground," Parry said, ruling out the possibility that the council could vote to send in troops.
"An armed intervention force ... isn't something which is on the agenda," he said.
The Guardian newspaper cited a British official saying London was drawing up plans to send soldiers if needed.
Jan Pronk, Annan's new envoy for Darfur, briefed the Security Council on the "extremely complex" situation.
"If these commitments really will be implemented, then the situation of the people in Darfur will indeed improve," Pronk said. "The international community has to go for implementation."