He plans to step down on Aug 31.
Secretary-general Ban Ki-moon said he accepted the resignation with “deep regret.”
Annan said he accepted the role when it seemed the international community, led by the UN Security Council, could help end the violence, enforce a ceasefire and bring about a political transition.
But the former UN secretary-general told reporters he cannot go on when the 15-nation council provides no backing for his role, particularly because of the stand-off between its five veto-wielding members: Russia and China on one side, the US, Britain and France on the other.
He was appointed special envoy in February of last year.
“When the Syrian people desperately need action, there continues to be finger pointing and name calling in the Security Council,” he told reporters.
“It is impossible for me or anyone to compel the Syrian government and also the opposition to take the steps to bring about the political process.”
“As an envoy, I can’t want peace more than the protagonists, more than Security Council or the international community, for that matter,” he added.
Annan said the failed six-point plan commonly referred to as the Annan plan is, in fact, the Security Council’s plan.
He did not rule out the idea of a successor being appointed by the current UN secretary-general, Ban Ki-moon, since “the world is full of crazy people like me, so don’t be surprised if someone else decides to take it on.”
Ban said in a statement he is discussing possible successors with the Arab League.
Russia’s UN envoy Vitaly Churkin said that Moscow regrets the decision to step down, according to the RIA Novosti. But Churkin also said he was encouraged by Ban’s search for a replacement.
Meanwhile Arab countries have dropped a demand that Syrian president Bashar Assad resign in the latest draft of a symbolic UN General Assembly resolution that faces a vote today.
The weakening of the resolution, which is not enforceable, showed the struggle to build an effective diplomatic approach to Syria’s civil war.
British Prime Minister David Cameron called on the UN to “ramp up” pressure on the regime of Syrian president Bashar Assad, after Annan’s resignation .
Cameron said that the development showed that the Annan plan has not worked.
Russia and China have blocked British-backed resolutions in the Security Council to threaten the Assad regime with global sanctions if it fails to halt the bloodshed in the 17-month uprising.
There was little sign of progress on the issue in Downing Street talks between Cameron and Russian president Vladimir Putin yesterday, after which the two leaders said only that Moscow and London would continue dialogue.
Speaking shortly after the announcement of Annan’s resignation, Cameron said: “The Annan plan — he has worked very hard at it, but it hasn’t worked, because we’ve got this appalling bloodshed, we’ve got this slaughter.
“I think what we need to do is actually ramp things up. We need to pass resolutions at the United Nations to put further pressure on Syria. I want to see them under so-called Chapter VII (of the UN Charter), so they have full legal backing of the UN — sanctions, travel bans, asset freezes, all the steps we can take to add to the pressure on the Syrians.”
On his first visit to Britain for seven years, Putin pledged to work to bring the conflict to an end.
But after 45 minutes of talks at his Downing St residence, Cameron acknowledged there was still a gulf between the two countries’ stances on Bashar al-Assad’s regime.
Britain has been strongly critical of Russia’s action to block UN action on the Syrian conflict, which human rights monitors say has killed 20,000 people.
Putin made no direct reference to Russia’s continuing support for Assad, but said there were some areas where Moscow and London “see eye-to-eye”.
“We agreed to continue working to find a viable solution,” he said.