Moscow (CNN) -- A leading Syrian opposition group called Tuesday for the introduction of U.N. peacekeepers in Syria after talks with Russian government officials, according to the Russian news agency Interfax.
Syrian National Council chairman Burhan Ghalioun also urged Russia to demand Syrian President Bashar al-Assad's resignation, according to Interfax, after a meeting at the Russian Foreign Ministry.
The talks came as another Syrian opposition group, the London-based Syrian Observatory for Human Rights, told CNN that 81 people had died in clashes Monday, which would make it one of the deadliest days of the uprising.
Ten more people, including two children, were killed Tuesday in the cities of Hama, Homs and Idlib, the Local Coordination Committees said.
The group also reported a heavy security presence in Idlib and Damascus suburbs, violent incidents at a number of universities and clashes in Daraa, where a group of army members had defected.
Al-Assad has become increasingly isolated in recent weeks as his Arab neighbors have added their voices to wide international condemnation of his government's crackdown on pro-democracy protests.
Gulf Arab countries rejected Tuesday a call from Damascus for a special summit to discuss the situation. "Holding an Arab summit at present is pointless," said Abdul Latif al-Zayani, the head of the Gulf Cooperation Council, according to the Kuwait News Agency.
Syria's former ally Turkey also added to the pressure Tuesday, threatening to cut off power supplies if Syria did not change course.
Ghalioun, in a news conference held at Interfax's Moscow office, said that the Syrian National Council was not asking for military intervention but rather "blue helmet" peacekeepers from the United Nations.
The peacekeepers were needed to ensure the safety of civilians and allow journalists free access to the country, Ghalioun said.
The position taken by Russia has given Syria a sense of protection from international criticism, Interfax quoted him as saying. Russia has previously accused the West of inciting opposition to the Syrian government and recently joined China in vetoing a proposed United Nations Security Council resolution to punish Syria for alleged human rights violations.
Ghalioun said both sides saw their talks in Moscow as "very positive," and that they had agreed to continue talking, the news agency said. The opposition group does not intend to talk to al-Assad or his family, however, Ghalioun was quoted as saying.
Russia's Foreign Ministry said in a statement that it was calling on all Syrian opposition groups to renounce violence and settle the crisis through peaceful dialogue with the Syrian government.
The Foreign Ministry had informed the Syrian National Council activists of the "unacceptability of outside military intervention in Syrian affairs," the statement said.
Meanwhile, the Syrian government freed 1,180 detainees Tuesday who were involved in recent events in Syria but did not commit murder, the state news agency SANA said. Their release comes 10 days after 553 prisoners were freed as the country marked the Muslim festival of Eid al-Adha.
The release of prisoners was among the proposals set out by the Arab League in a peace plan for Syria earlier this month.
But the Arab League decided Saturday to suspend Syria's membership after it failed to stick by its pledges.
The suspension, a blow to al-Assad which was welcomed by the Syrian National Council, is due to go into effect Wednesday.
The league also called for unspecified sanctions against Syria and called on member states to withdraw their ambassadors from Damascus, a decision that will be up to each nation.
The punitive measures came after al-Assad's failure to abide by an Arab League proposal earlier this month to halt all violence, release detainees, withdraw armed elements from populated areas and allow unfettered access to the nation by journalists and Arab League monitors.
Well over 3,500 people have been killed in the eight months since the uprising began, according to the Office of the United Nations High Commissioner for Human Rights.
In the darkness of the early hours of Tuesday, Syrian government forces and anti-Assad militants fought in two towns south of the capital, Damascus, the Syrian Observatory for Human Rights said in a statement.
"Witnesses said heavy guns are used after four large explosions were heard at a military center that lies between Sanamein and Inkhel," it said.
The battle has taken a toll on life and limb, said the observatory, which also cited eyewitness reports of "heavy gunfire" in other Syrian towns.
Fighting also continues along the Jordanian border between the Syrian security forces and anti-Assad militants, the observatory said.
The latest reported violence came a day after Jordan's King Abdullah said that he would step down if he were Bashar al-Assad, a statement observers interpreted as a call for the Syrian president to do just that.
"If Bashar has the interests of his country, he would step down, but he would also create an ability to reach out and start a new phase of Syrian political life," Abdullah told the BBC.
In Amman, Jordan, about 300 people assembled spontaneously after midnight Tuesday in front of the Syrian Embassy in support of Abdullah's statement, one of the protesters said.
Many who gathered were Syrians living in Jordan, said protester Obaydah Amer.
A few hours after the Jordanian king's statement, Petra, the state-run news agency, said Abdullah's remarks "were not a direct call for the Syrian president to step down but he was, rather, responding to a question on what can a person in his position do."
Large pro-government demonstrations have also been held in the region by al-Assad supporters.
CNN's Alla Eshchenko, Tracy Doueiry and Jack Maddox contributed to this report.