A firefight broke out Monday in Damascus, sparking one of the fiercest clashes in the capital since the conflict between Syria's opposition and government forces began a year ago.

According to reports, heavy fire from machine guns and rocket-propelled grenades could be heard as rebels fought government forces in the closely guarded al-Mezze district.

Also Monday, the head of the International Committee of the Red Cross was in Moscow urging Russian officials to press Syria's President Bashar al-Assad to give humanitarian-aid convoys greater access to residents trapped by fighting.   

The latest violence in Damascus followed car bomb explosions that targeted military-intelligence facilities in the capital and another city, Aleppo, over the weekend. Authorities blamed those attacks on terrorists, according to the Associated Press.

There is fighting near Hamada supermarket and the sound of explosions there and elsewhere in the neighborhood. Security police have blocked several side streets and the street lighting has been cut off, a housewife in al-Mezze was quoted as saying by Reuters.

According to witnesses, security forces beat and arrested people who gathered in Damascus on Sunday to mourn the victims of the car bomb blasts.

Among those arrested was Mohammed Sayyed Rassas, leader of the National Coordinating Body for Democratic Change, which has been insisting on nonviolent means to overthrow Assad's government.

Until now, Damascus had largely escaped the fighting that enveloped other parts of Syria.

The violence demonstrates the shifting nature of the year-old conflict, with rebels possibly trying to distract from government successes in clearing the city of Homs and other former rebel strongholds.

On Monday, security forces stormed an apartment used as a hideout by an armed terrorist group in al-Mezze, state-run news agency SANA said.

At least three people were reported killed in Monday's fighting.

In Moscow, the head of the Red Cross, Jakob Kellenberger, was pushing for Russia's support of a daily two-hour cease-fire in Syria so that aid and humanitarian workers could get to people affected by the fighting.

Our assessment, unfortunately, is that the humanitarian situation is most likely to deteriorate, Kellenberger told Russia's Foreign Minister Sergei Lavrov at the start of talks, according to Reuters.

Russia and China have vetoed two United Nations Security Council resolutions condemning the Assad regime.