British Prime Minister David Cameron said Annan's resignation was evidence that the current approach has failed — and that the U.N. needs to get tougher with Syria.
"We've got this appalling bloodshed. I think what we need to do is to ramp things up," Cameron told Sky News television.
U.N. Secretary-General Ban Ki-moon said he accepted the resignation with deep regret, and is discussing possible successors with the Arab League. "I remain convinced that yet more bloodshed is not the answer; each day of it will only make the solution more difficult while bringing deeper suffering to the country and greater peril to the region," Ban said.
Russia's U.N. envoy Vitaly Churkin said Moscow also regrets Annan's departure but is encouraged by Ban's search for a successor, the RIA Novosti news agency reported.
Asked about the idea of a successor being appointed, Annan said, "The world is full of crazy people like me, so don't be surprised if someone else decides to take it on."
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