UN leader Ban Ki-moon said Syria is heading toward an "imminent" civil war and highlighted growing attacks on UN observers.
Annan renewed calls for the major powers to warn Assad of "clear consequences" if he does not comply with a six-point international peace plan, one diplomat inside a closed-door council briefing told AFP.
"The longer we wait, the darker the future looks for Syria," another diplomat quoted Annan as telling the council.
Annan called for "united" and "substantial" pressure on Assad. He said there must be "real results soon or the crisis will spiral out of control."
After the meeting, Ban told reporters, "Syria can quickly go from a tipping point to a breaking point. The danger of a full-scale civil war is imminent and real, with catastrophic consequences for Syria and the region."
"The Syrian people are bleeding. They are angry. They want peace and dignity. Above all, they all want action," Ban told reporters.
The meeting was held only hours after the latest massacre in Syria which Ban and Annan condemned.
UN monitors fired upon
Shots were fired at the UN convoy which tried to get into the village of Al-Kubeir to investigate the slaughter, Ban said.
Heavy weapons, armor-piercing bullets and surveillance drones have been used against UN observers to hamper their efforts to monitor the worsening conflict, Ban told the meeting.
The tactics had been used to try to force the unarmed monitors to withdraw from areas where government forces have been accused of staging attacks, Ban was quoted as saying.
Ban said the heavy shelling had been used to deter a UN Supervision Mission in Syria (UNSMIS) convoy, drones had monitored the movements of observers and the armor-piercing bullets had been fired at UNSMIS vehicles.
According to UN officials, UN vehicles are shot at almost every day in Syria. At least two roadside bombs have also targeted UN convoys since the mission started.
Ban praised the "brave" monitors but said the Security Council would have to consider whether the mission is "sustainable".
UN observers had seen Syrian military convoys approaching villages and tried to stop tank assaults against populated areas, but had been "ignored", Ban said.
According to preliminary evidence, the Syrian army had surrounded the village, and militia had entered Al-Kubeir and killed civilians with "barbarity", Ban was quoted as telling the Security Council.
UN monitors had been prevented from going into Al-Kubeir but would make a new attempt to enter the village on Friday, UN spokesmen said.
Iran's help sought
Annan said he was in discussions to set up an international contact group on the Syria crisis and that he hoped Iran would be part of the "solution".
US ambassador Susan Rice said however that Iran was a "spoiler" and "part of the problem in Syria"
"There is no question that it is actively engaged in supporting the government in perpetrating the violence on the ground," Rice told reporters.
"Iran has not demonstrated to date a readiness to contribute constructively to a peaceful political solution."
The Security Council has passed two resolutions which approved the UN monitoring mission in Syria and condemned the violence there. But it is divided over how to increase pressure.
Russia, Syria's last major ally, and China have vetoed two council resolutions which only hinted at future sanctions. The United States and European nations want economic sanctions on Assad.
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Not only the brutality in Syria is spiralling out of control, Assad's militiamen demonstrated their immense hatred towards the Sunnis. Even butchering the people didn't satisfy the blood lust of the attackers, they hadn't spared the livestock neither.