The international envoy has left Syria without a deal to end the year-old conflict in the country, as regime forces mounted a new assault on rebel strongholds in the north.
The former UN secretary general said he had presented the Syrian president, , with concrete proposals "which will have a real impact on the ground".
"Once it's agreed, it will help launch the process and help end the crisis on the ground," he said at the end of a two-day visit.
Annan, who also met Syrian opposition leaders and business leaders in Damascus, said he was optimistic following two sets of talks with Assad, but acknowledged that resolving the crisis would be tough. "It's going to be difficult but we have to have hope," he said.
He called for reforms that would create "a solid foundation for a democratic Syria". But he said: "You have to start by stopping the killing and the misery and the abuse that is going on today and then give time for a political settlement."
The US secretary of state, Hillary Clinton, and the Russian foreign minister, Sergei Lavrov, are due to meet in New York on Monday on the sidelines of a special UN security council ministerial meeting on Arab revolts, with likely to be a central topic. Others taking part in the council session include William Hague and France's Alain Juppe.
In his discussions with Assad on Saturday, Annan made several proposals to end the political crisis and start a political dialogue. Assad told Annan that a political solution was impossible as long as "terrorist groups" threatened the country.
The opposition's leadership has also rejected dialogue, saying talk is impossible after a crackdown that the UN estimates has killed more than 7,500 people.
Syrian forces kept up an offensive against rebel strongholds in the north and shelled neighbourhoods in the central city of Homs, as well as clashing with rebel fighters across the country.
Military units loyal to Assad appear to have been freed up after crushing lightly armed rebels in the Baba Amr district in Homs last week, and are on the attack in Idlib province, across the border from key opposition supply bases in Turkey.
A Turkish official said the violence had led to a rise in Syrian civilians fleeing to Turkey. Some 1,000 had crossed the border in the past week, compared with 1,000 in the previous month, the official said.
In Homs, several activists reported intense shelling of the Karm el-Zeytoun, Bab Dreib and Job al-Jandali districts and said several people were killed.