The Syrian government has welcomed Lakhdar Brahimi, the new international Syrian envoy, as have most players in the conflict.
The office of Farouk al-Sharaa, Syria's vice-president, said in a statement on Saturday that it "supports Brahimi's demand to get united support from the Security Council to carry out his mission without obstacles".
The 78-year-old Algerian, whose previous missions include Iraq, Afghanistan and South Africa, UN told Al Jazeera on Friday he faces a huge task to end the violence in the country.
Some experts are saying Brahimi faces an impossible mission, and the UN has already admitted both sides appear set on war.
Brahimi told Al Jazeera he faces a huge task to end the violence in the country but that he could not turn down the job.
"We will go into this with a lot of good will, a lot of hope, but a lot of humility as well," he said by phone on Friday.
"The United Nations, and I supposed the Arab League as well, simply cannot just say 'This is a difficult job, let's look away'," he said.
"I don't know if there's any conflict that hasn't ended with some kind of negotiation, with some kind of diplomatic phase."
Hillary Clinton, the US secretary of state, on Friday endorsed Brahimi in his new role.
Clinton said the international community "remains fully committed" to bringing about change in Syria, where activists say more than 23,000 people have died during the brutal crackdown by President Bashar al-Assad's regime.
"My message to Special Envoy Brahimi is simple: The United States stands ready to support you and secure a lasting peace that upholds the legitimate aspirations for a representative government of the people of Syria," Clinton said in a statement.
"And to the Syrian people: you are not alone."
The top US diplomat, who said she "welcomes" the decision to appoint Brahimi, insisted that "the international community remains fully committed to a Syrian-led political transition leading to a pluralistic political system representing the will of the people".
Earlier, White House deputy press secretary Josh Earnest said officials in Washington "need to hear more from the UN on the mandate of Mr Brahimi's new position".
Britain said it "fully supports" Brahimi's appointment, welcoming the "vast experience" he brought to the role of seeking a political solution to the violence.
Annan is stepping down at the end of this month after sharply criticising world powers for the failure to agree an approach to ending the violence in Syria.
In-depth coverage of escalating violence across Syria
Ban Ki-moon, the UN secretary-general, appealed to the divided international community to give "strong, clear and unified" support to the new envoy.
"The secretary-general appreciates Mr Brahimi's willingness to bring his considerable talents and experience to this crucial task for which he will need, and rightly expects, the strong, clear and unified support of the international community, including the Security Council," Eduardo del Buey, his spokesperson, said.
Russia, Assad's main ally, and China have vetoed three UN Security Council resolutions on Syria, accusing Western nations of only seeking forced regime change.
Brahimi, who hesitated for days to accept a job that France's UN envoy Gerard Araud called an "impossible mission", will have a new title, Joint Special Representative for Syria.
Diplomats said the change was to distance himself from the frustrations experienced by Annan during his mission, and that Brahimi has the support of all Security Council members.
Brahimi told Al Jazeera he would be speaking to all parties involved in the negotiations to try to ensure he would have their full co-operation.
"[Annan's] resignation is a very important act in favour of the Syrian people. Because what he said to the people who tasked him is that 'Look, you asked me to do a job and you didn’t give me the tools; the tools being your support'," he said.
Council diplomats said privately that it will be extremely difficult for Brahimi to transform the expressions of support into a binding sanctions resolution that would pressure the government and rebels to stop fighting.
Annan had urged the council to adopt such a resolution, but Russia was opposed.
Separately, Russia canceled a meeting on Friday of the permanent council members and key Middle Eastern nations on Syria, the so-called Syria "Action Group", after most participants failed to confirm attendance, UN diplomats said.
"Almost no one confirmed attendance, not the Americans, Europeans, Arabs," one diplomat told Reuters on condition of anonymity.
"There wasn't much interest in this meeting."