(CNN) -- The U.N. point man on Syria said Friday that he's working hard to stop the yearlong violence there and "get unimpeded access" for humanitarian relief.
"I'm doing my best with the support of everyone to try to find a peaceful solution," Kofi Annan, special joint U.N-Arab League envoy, told reporters Friday from Geneva after a private teleconference with the U.N. Security Council. "The Syrian people want to get on with their lives. They are tired and they suffered a lot."
He said U.N. humanitarian agencies are to arrive in Syria this weekend "if they are not there already, to start their mission with the Syrian government."
Annan met last weekend with Syrian President Bashar al-Assad in Damascus and the Syrian opposition in Turkey in an effort to end the violence that has swept the nation since Syrian security forces cracked down on protesters a year ago. He described the atmosphere in the talks as "welcoming and correct."
"We are continuing our discussions" with the government, Annan said. He is also sending the mission this weekend to Damascus "to pursue the discussions and the proposals we left on the table, and at the appropriate time, when I deem sufficient progress has been made, I shall be prepared to go back to the region."
Annan said he spoke with opposition members who are "keen to get talks going and resolve the issue politically and peacefully."
"They are impatient," he said. "The killings are going on over (a) year now."
The former U.N. secretary-general said the situation in Syria is "much more complex" than that in Libya or other nations. "It's a conflict in a region of the world that has seen many, many traumatic events. I think we need to handle the situation in Syria very, very carefully," he said. "Any miscalculation that leads to major escalation will have impact in the region."
Asked about the prospects of a coalition government, Annan said such a development would have to emerge from talks among Syrians.
U.N. Security Council members are backing Annan's efforts, said Mark Lyall Grant, the British ambassador to the United Nations and the current council president.
Grant didn't disclose details about the meeting but told reporters the session was "comprehensive."
"All council members pledged their full support for Mr. Annan and his mission," he said. "Clearly it is the primary responsibility of the Syrian government to stop the killing of its own citizens. It is the Syrian government that has the heavy artillery, that has the heavy weaponry and therefore the responsibility is on them to stop the killing first."
Bashar Jaafari, the Syrian ambassador to the United Nations, also told reporters that "Syria is committed to making Mr. Annan's mission successful."
Annan's moves occurred as shelling and arrests in the country intensified and peaceful marchers took to the streets Friday in nationwide protests calling for "immediate military intervention," the theme of the day's demonstrations and a reference to opposition calls for outside military intervention.
Most reports from inside the country indicate the regime is slaughtering civilians to wipe out dissidents seeking al-Assad's ouster. The al-Assad family has ruled Syria for more than four decades.
But al-Assad's regime has said "armed terrorist groups" are behind the bloodshed in Syria and says it has popular support for its actions.
The Syrian government Friday underscored its position on terror in letters to top U.N. officials, including U.N. Secretary-General Ban Ki-moon. The government said it is protecting its citizens from "terrorists" who are slaughtering and murdering "innocent citizens."
The government said that terrorist groups committed a "massacre" Monday in some neighborhoods of the city of Homs that claimed the lives of about 45 citizens. The letter said there had been "atrocities" in other cities as well, the state-run Syrian Arab News Agency said.
"Terrorists have slaughtered and murdered innocent citizens and photographed and sent it to the stations and satellite channels that contribute to the misinformation and straining the situation and their work is incompatible with the values of substantive information and distort the facts and support terrorism," the ministry said.
The government said Syria is working to find a political solution to the crisis and wants to cooperate with Annan. It argues it has initiated "democratic achievements" over the past year, citing the abolition of the state of emergency, the issuance of the law of multiparty politics and local election law, the issuance of the new constitution and other reforms.
Across Syria, opposition activists said gunfire or explosions could be heard early Friday in several suburban cities in the Damascus region.
Security forces were arresting people in the northeastern city of Deir Ezzor, activists said. Security forces gunned down one civilian, according to the Syrian Observatory for Human Rights.
There was shelling in Homs for the seventh consecutive day, a resident said.
"Thousands have fled to other city districts and nearby villages and towns," said Abu Mousab of Homs. "What we fear the most is the sporadic shelling."
Four armed military defectors died as in clashes with regime forces in Daraa province, the Syrian Observatory for Human Rights said.
CNN cannot independently confirm reports of casualties or attacks in Syria because the government has severely restricted the access of international journalists.
The violence began last March, when Syria launched a crackdown against protesters who were peacefully airing their grievances. The crackdown spiraled and spurred a nationwide anti-government movement.
Political opposition groups, including the Syrian National Council, and fighters such as the Free Syrian Army, have emerged and become key players in the opposition movement. More than 8,000 people have died in the conflict, according to the United Nations, but opposition activists said the overall toll is more than 9,000, most of them civilians.
One of the pressing issues is the fate of civilians caught in the crossfire.
Officials from the United Nations and the Organization of Islamic Cooperation plan to go on a mission led by the Syrian government to the provinces of Homs, Hama, Tartous, Latakia, Aleppo, Deir Ezzor, Rif Damashq and Daraa to assess humanitarian needs.
"There is no time to waste," said Valerie Amos, the U.N. humanitarian chief. "It is increasingly vital that humanitarian organizations have unhindered access to identify urgent needs and provide emergency care and basic supplies."
Workers from the Syrian Arab Red Crescent and the International Committee of the Red Cross assessing the humanitarian situation in the Homs province reported 12,000 displaced people in the town of Al Zaafaraneh, an ICRC official said.
People who fled the Homs communities of Rastan, Talbiseh, Baba Amr and Karm al Zaytoun took refuge in the town. They need food, medicine, mattresses and blankets, said Sean Maguire, ICRC spokesman in Britain.
Many world powers have denounced the crackdown and demanded that al-Assad leave office, and some politicians across the globe, including U.S. lawmakers, have raised the possibility of armed intervention.
Russia, which vetoed a tough U.N. resolution against the regime, said it will never support "military intervention against Syria while forging a decision in the U.N. Security Council."
CNN's Amir Ahmed and Joe Sterling contributed to this report.