A nonbinding statement approved by the 15 council members and read at a formal meeting spells out Annan's proposals which include a cease-fire first by the Syrian government, a daily two-hour halt to fighting to evacuate the injured and provide humanitarian aid, and inclusive Syrian-led political talks "to address the legitimate concerns of the Syrian people."
In a bid to win support from Russia and China, which have twice vetoed European and US-backed resolutions condemning President Bashar Assad's crackdown on protesters, France watered down the statement to eliminate possible consideration of "further measures" which could include sanctions or military action.
Instead, the presidential statement now asks Annan to update the council regularly on the progress of his mission and says that "in the light of these reports, the Security Council will consider further steps as appropriate."
A presidential statement, which needs approval from all council members, becomes part of the council's permanent record. It is stronger than a press statement, which does not. But unlike resolutions, neither statement is legally binding.
The governments of the 15 council nations had been given until 9 a.m. (1300 GMT) Wednesday to raise any objections to the text of the statement. No country did so.
Russia and China had called the earlier resolutions unbalanced, saying they demanded an end only to government attacks, not ones by the opposition. Moscow also argued that the resolutions promoted regime change in Syria and expressed fear of outside intervention to support the rebels, as happened in Libya.
"The most important (thing) is that there are no ultimate demands there, there are no threats, and no theses which would predetermine who carries more guilt," Russian Foreign Minister Sergey Lavrov said of the statement in Berlin, where he met his German counterpart.
France's UN Ambassador Gerard Araud said, "It's not a question of threat or of ultimatum. We are expressing our support to Mr. Kofi Annan."
Germany's UN Ambassador Peter Wittig and US Ambassador Susan Rice expressed hope that agreement on the statement would lead to greater unity in the council on Syria, where well over 8,000 people have died in violence over the past year, according to the UN.
"We hope that this will change the dynamic on the ground," Wittig said. "This is a newly found unity of the council which we welcome after this rather sad track record of the two double-vetoes in the past, and it shows nobody can really have an interest of mayhem in the region."
Rice called the presidential statement "a modest step ... forward" and urged Syrian authorities "to respond swiftly and positively."
UN Secretary-General Ban Ki-moon said Tuesday that the Syria crisis is the most pressing issue facing the world.
"We have no time to waste, no time to lose. Just one minute, one hour delay will mean more and more people dead," Ban told reporters in the Indonesian city of Bogor, his first stop on an Asian tour.
One of the sticking points among Russia, Syria and the West is the sequencing of a cease-fire. Syria says the opposition must lay down its arms first. Russia says the government and opposition must stop fighting simultaneously. Western countries insist that since Assad's forces started fighting first and are responsible for most of the killings, they must stop first.
The revised draft resolution would require the Syrian government to immediately stop troop movements and halt the use of heavy weapons in populated areas. As these actions are taking place, it says the government should work with Annan to bring about a halt to violence under UN supervision.
The draft says Annan should seek similar commitments from the opposition - with no mention of a time frame.
Annan, the joint UN and Arab League envoy, met twice with Assad on March 10-11 and has sent a team to Damascus to discuss implementation of his six-point proposal.
Russia's UN Ambassador Vitaly Churkin said Annan's team is having "good discussions with the Syrian government" but he said there is "a missing link" because the presidential statement calls for engagement with the opposition and opposition armed groups, "and so far I'm not aware of much success in engaging them."
"This, of course, is something which is going to be crucial if the Syrian-led political process is established with the help of Mr. Annan," he said.
The Security Council also issued a press statement proposed by Russia that "condemned in the strongest terms the terrorist attacks" in Damascus on Saturday and Monday and in Aleppo on Sunday, "causing scores of death and injuries." It characterizes the attacks by the Syrian opposition forces as "terrorism."