The Syrian state news agency, SANA, says two rebels and a security force member were killed in Monday's pre-dawn battle that frightened residents of the Mazzeh neighborhood, which is home to embassies and senior government officials.
It was the closest fighting to the center of Damascus since the start of Syria's year-long opposition uprising against President Assad's autocratic rule.
SANA says the fighting began when security forces stormed a Mazzeh apartment used as a hideout by what it called an "armed terrorist" group. Syrian authorities say the uprising is driven by terrorist gangs carrying out a foreign conspiracy to topple President Assad.
The Britain-based Syrian Observatory for Human Rights said several "armed groups of defectors" entered Mazzeh from outlying areas of Damascus and fired a rocket-propelled grenade at the house of an army brigadier general. It said the ensuing battle killed at least three rebels and wounded 18 government soldiers.
There was no independent confirmation of the casualties or how the Damascus fighting started. But, it was a show of force by the rebels after pro-Assad troops recently drove them out of opposition strongholds in the central city of Homs and the northern city of Idlib.
Russia said Monday the Syrian government and its armed opponents should immediately start observing daily humanitarian truces to enable the International Committee of the Red Cross to evacuate civilians and treat the wounded in areas affected by fighting.
The Russian government made the statement after ICRC president Jakob Kellenberger met with Russian Foreign Minister Sergei Lavrov in Moscow. Kellenberger made the trip to urge Russia to use its influence as a Syrian ally to press the Assad government to lay down its arms for several hours a day.
Arab League mission
The U.N.-Arab League special envoy for Syria, Kofi Annan, sent a five-member team to Damascus on Sunday to begin talks with Syrian officials on implementing his plan for ending the country's conflict. A spokesman for Annan says the international experts will stay in Syria as long as they are making progress in reaching agreements on a cease-fire between the government and the rebels and starting a national dialogue.
France proposed a U.N. Security Council statement expressing full support for the work of Annan and his team. Diplomats said Western powers backing the draft presidential statement hope it will be adopted on Tuesday.
In other developments on Monday, witnesses and activists said Syrian government troops and tanks carried out raids in the eastern region of Deir al-Zor and the northern region of Idlib to try to drive out rebels of the Free Syrian Army.
The United Nations says at least 8,000 people have been killed in the Assad government's violent crackdown on the revolt, which began with peaceful protests and became increasingly militarized as army defectors attacked pro-Assad troops who assaulted civilians.
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Some information for this report was provided by Reuters.