The EU foreign affairs chief Catherine Ashton has called for a rapid appointment by the UN and the Arab League of a successor to Kofi Annan.
It comes after he quit as Syria's peace envoy earlier today.
Mr Annan has complained that his cease fire - which aimed to bring peace to the war-torn country - has not been upheld by either party caught up in the violence.
The British Prime Minister David Cameron has said that diplomatic efforts now need to be stepped up by the international community.
"Syria isn't Libya it's a different situation, I don't think military approaches are right in this case, I have thought very carefully about that", he said
"But I think there is a lot more pressure we can put on".