Rodrigo Abd / AP
Women and children take shelter from fierce fighting between the Free Syrian Army and government troops in Idlib, north Syria, on Saturday.
Updated 12:15 p.m. ET: BEIRUT -- U.N.-Arab League envoy Kofi Annan said it would be hard to reach a deal to halt bloodshed in Syria, but expressed optimism after meeting President Bashar al-Assad for a second day on Sunday.
"It's going to be tough. It's going to be difficult but we have to have hope," he told reporters in Damascus.
"I am optimistic for several reasons," Annan said, citing a general desire for peace in Syria. "The situation is so bad and so dangerous that all of us cannot afford to fail."
Khaled Al-Hariri / Reuters
U.N. envoy Kofi Annan, left, and Syria's Foreign Minister Walid al-Moualem enter a restaurant to attend a working lunch in Damascus on Saturday.
The former United Nations chief, who is from Ghana, said: "I have urged the president to heed the African proverb which says: 'You cannot turn the wind, so turn the sail.' "
Annan, speaking before departing for Qatar, said he had left "concrete proposals" with Assad for a way out of a conflict that has cost thousands of lives.
"You have to start by stopping the killings and the misery and the abuses that are going on today, and then give time (for a) political settlement," he said.
There was no immediate word from Syrian officials on the outcome of the talks, but Assad told Annan on Saturday that "terrorists" spreading chaos and instability were blocking any political solution, according to the state news agency SANA.
But it said the 46-year-old president had also told Annan he would help in "any honest effort to find a solution".
Syrians involved in a popular uprising against Assad say there can be no meaningful dialogue with a leader who has inflicted such violence and suffering on his own people.
"Him (Assad) stepping down is definitely a first condition of any discussion or negotiation," Bassma Kodmani of the opposition Syrian National Council told the BBC on Sunday.
The United Nations says Assad's forces have killed more than 7,500 people in a year-long crackdown on protesters and insurgents. Authorities say rebels have killed 2,000 soldiers.
Annan's mission has coincided with a Syrian military offensive against opposition strongholds in the northwest.
Activists said at least four people were killed in the town of Idlib on Sunday after troops and tanks moved in a day earlier. Three soldiers and a civilian were also killed in fighting in the village of Janoudiya in Idlib province on Sunday morning, according to the Syrian Observatory for Human Rights.
State news agency SANA said "terrorists" shot dead a former boxing champion, Ghiath Tayfour, in the city of Aleppo and also killed a leading Baath Party member in Homs province.
The Observatory said 39 civilians, including 25 in Idlib province, were killed on Saturday, along with 39 rebels and 20 government soldiers, giving an overall death toll of 98.
Russian Foreign Minister Sergei Lavrov, who met Annan in Cairo on Friday, told the Arab League his country was "not protecting any regime," but did not believe the Syrian crisis could be blamed on one side alone.
He called for a ceasefire and humanitarian aid access, but Qatar and Saudi Arabia sharply criticized Moscow's stance.
Qatari Prime Minister Sheikh Hamad bin Jassim al-Thani, who has led calls for Assad to be isolated and for Syrian rebels to be armed, said a ceasefire was not enough. Syrian leaders must be held to account and political prisoners freed, he declared.
Saudi Foreign Minister Saud al-Faisal said shortcomings in the U.N. Security Council, where Russia and China have twice vetoed resolutions on Syria, had allowed the killing to go on.
Their position, he said, "gave the Syrian regime a license to extend its brutal practices against the Syrian people."
Saudi Arabia and Qatar, which are both ruled by autocrats and espouse a strict version of Sunni Islam, are improbable champions of democracy in Syria. Riyadh has an interest in seeing Assad fall because this could weaken its Shi'ite regional rival Iran, which has been allied with Syria since 1980.
International rifts have paralyzed action on Syria, with Russia and China opposing Western and Arab calls for Assad, who inherited power from his father nearly 12 years ago, to quit.
The United States has drafted a fresh U.N. Security Council resolution, but Washington and Paris have said they are not optimistic it will be accepted.
Despite their differences, Lavrov and Arab ministers said they had agreed on the need for an end to violence in Syria.
They also called for unbiased monitoring of events there, opposition to foreign intervention, delivery of humanitarian aid and support for Annan's peace efforts.
But the exiled opposition Syrian National Council ruled out talks while Assad is in power.
"Negotiations can never take place between the victim and torturer: Assad and his entourage must step down as a condition before starting any serious negotiations," it said.
U.S. Secretary of State Hillary Clinton will meet Lavrov in New York on Monday when the Security Council holds a special meeting on Arab revolts, with Syria likely to be in focus.
Syrian forces have been building up for days around Idlib, the capital of a hilly, agricultural province along the Syria-Turkey border that has been a hotbed of protests against Assad's regime.
Saturday morning, troops blasted Idlib for hours with dozens of tank shells as the forces moved to encircle the town, an Associated Press team in Idlib reported.
Families fled their homes, carrying blankets and a few other meager belongings. Others huddled in homes.
The Idlib operation raised fears that Assad is set to launch an all-out offensive in Idlib like the one that captured captured part of Homs in the south.
Reuters and The Associated Press contributed to this report.