Mr Annan is now the UN and Arab League Envoy to the country, and he was speaking as violence in Syria continued. This was despite the deadline for a withdrawal of troops from populated areas having passed.
Reports show that over 100 people were killed in fighting yesterday, with fresh shelling taking place in the embattled city of Homs. Meanwhile, there have also been reports in Turkey of gunfire across their border with Syria, aimed at a refugee camp for escapees in Turkey.
President Bashar al-Assad has said he’s still seeking assurances from rebels that the fighting will stop from their side in the ceasefire plan. However despite this, Kofi Annan says he’s hoping fighting will stop by Thursday morning.
"If everyone respects it I think by six in the morning on Thursday we shall see improved conditions on the ground," he said.
He added that any mistakes or miscalculations in the Syrian situation could have “unimaginable consequences”.
Mr Annan was speaking in Tehran, where he was appealing for support from Iran’s Foreign Minister Ali Akbar Salehi. Iran has been a key ally of Syria in recent years, but Mr Salehi stated that if the peace plan continued in the way it has been, Iran would fully support it.