Ban's announcement came a day after Western powers agreed to change the proposed Security Council statement on the year-old crisis in Syria when Russia refused to back any "ultimatum" to President Bashar al-Assad.
UN-Arab League envoy Annan, who held talks in Damascus on March 10-11, "briefed the Security Council on Friday, and I expect him to return to Damascus very soon," Ban told a conference in Jakarta.
The UN secretary general outlined the priorities in Syria, where monitors say more than 9,100 people have been killed in a brutal crackdown on anti-regime protests.
"Our priorities are three: first an immediate end to the violence -- all violence -- and engage in inclusive political dialogue to shape the future of Syria as civilian people want to create, and thirdly we have to provide immediately and urgently humanitarian actions," he said.
On the ground on Tuesday, fresh clashes broke out in the capital and security forces killed at least 30 people, all but two of them civilians, in violence elsewhere across the country, the Syrian Observatory for Human Rights said.
A security clampdown in the capital followed what activists said was a hit-and-run attack in the heavily guarded Mazzeh neighbourhood on Monday that killed at least three rebels and a member of the security forces.
It also came on the heels of deadly twin suicide car bombings targeting security buildings in Damascus on Saturday.
Amid growing signs of a weakening of Moscow's support for Assad, Russian Foreign Minister Sergei Lavrov said the Syrian leader had made "a lot of mistakes" since peaceful protests broke out in mid-March 2011.
"We believe that the Syrian leadership responded incorrectly to the very first manifestations of the peaceful protests," he told Russia's Kommersant FM radio in a pre-recorded interview.
"The Syrian leadership -- despite the numerous promises it has made in response to our calls -- is making a lot of mistakes."
Russia said on Tuesday it was ready to back either a Security Council statement or resolution on UN-Arab League peace envoy Annan's proposals on ending the crisis as long as it contained no ultimatums.
At the United Nations, diplomats from the 15-nation Security Council held four hours of talks on a Western-drafted presidential statement.
Russia led resistance to part of the statement that said the council would "consider further measures" if Assad does not act upon the envoy's peace plan, diplomats said.
Russia and China have already vetoed two full resolutions on Syria.
The latest proposed statement, obtained by AFP, does not condemn the violence but would express "gravest concern" at the deteriorating crisis in Syria and "profound regret" at the thousands of dead.
France had expressed hope that the statement its submitted to the council -- which carries less weight than a full resolution -- could be adopted on Tuesday.
On Monday, a team of technical experts sent by Annan started talks in Damascus on a possible ceasefire and international monitoring mission as part of his peace efforts.
And a team from the United Nations and Organisation of Islamic Cooperation is taking part in a Syrian government-led humanitarian assessment mission to battered protest cities.
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