(CNN) -- Intense fighting between Syrian rebels and government forces erupted Monday in the Damascus neighborhood of al-Mazzeh, the site of embassies, security buildings and the homes of some members of the president's inner circle, opposition activists said.
At least 18 members of the security forces were injured, according to the opposition Syrian Observatory for Human Rights. The clashes were the fiercest so far in the Syrian capital, and the closest to its security centers since the start of the Syrian uprising last year, the group said.
The state-run Syrian Arab News Agency later said two "terrorists" and a member of the security forces were killed when authorities reaided an apartment building in the neighborhood, seizing machine guns and grenades in the process. A spokesman for the Free Syrian Army confirmed the rebels' involvement in the clashes but had no details.
The fighting in Damascus came as rebels made apparent gains against President Bashar al-Assad's forces elsewhere in the country. Meanwhile, a team of experts sent by the United Nations arrived in Syria, while Russia -- al-Assad's leading ally and arms supplier -- joined a Red Cross call for periodic truces to allow the delivery of humanitarian aid.
Russian Foreign Minister Sergey Lavrov met Monday with Jakob Kellenberger, the president of the International Committee of the Red Cross. Both men "expressed conviction that providing humanitarian aid to Syrians in need is an absolute priority at the current stage," a statement from the Russian Foreign Ministry recounted.
"Both sides called on the Syrian government and all armed groups of the opposition to immediately agree to daily humanitarian pauses in order to allow ICRC and Syria's Society of Red Crescent access to the wounded and other civilians who need to be evacuated," the statement read. "Medical personnel assisting in those actions must also be protected."
Kellenberger warned Sunday that the humanitarian situation across Syria continues to worsen after a yearlong campaign by al-Assad's forces against the country's domestic opposition. In Monday's statement, Moscow also repeated a call for the ICRC "to be able to access all those detained because of their participation in the protests in Syria."
Russia, along with China, has vetoed attempts by fellow U.N. Security Council members to pass resolutions condemning al-Assad regime for its clampdown. The two countries said they want the violence to stop, but argued that the resolution was not even-handed. Both have major trade deals with Syria.
U.N. officials say the Syrian campaign has claimed more than 8,000 lives, while opposition activists put the toll at more than 9,000 -- most of them civilians.
Syria's government blames "armed terrorist groups" for the violence. CNN cannot independently confirm reports of casualties or attacks in Syria because the government has severely restricted the access of international journalists, but most reports from inside Syria indicate the regime is slaughtering civilians to wipe out dissidents seeking al-Assad's ouster.
Monday, fighters from the rebel Free Syrian Army destroyed the Division of the Countryside, a government ministry, in the eastern area of Deir Ezzor, according to the Local Coordination Committees of Syria (LCC), an opposition activist network. The rebels battled government forces who subjected them to "intense shelling," the group said.
At least 34 people were killed Monday across Syria, the LCC said. Their count included 10 in Deir Ezzor; six in Daraa; five in Hama; three in Aleppo; three in Idlib; three in Damascus suburbs; and two each in Qameshli and Homs.
In addition, "several" security forces were killed when the Free Syrian Army attacked a security checkpoint in Qameshli, a northeastern city, the LCC said. The Free Syrian Army is made up largely of army defectors who are now battling the much larger, better-equipped forces that remain loyal to the government.
SANA said 20 people, including soldiers, police and civilians, were buried Monday after being killed by "terrorist groups." The victims were killed in Damascus and its suburbs, Idlib, Deir Ezzor and Homs, the report said.
Amid the violence, a five-member U.N. team with expertise in politics, peacekeeping and mediation was on the ground in Syria, according to Eduardo del Buey, deputy spokesman for the U.N. secretary-general. The team will stay as long as it is making progress toward goals set by Kofi Annan, the special joint U.N.-Arab League envoy to Syria, del Buey said.
The team's exact plans cannot be disclosed, he said.
The latest developments followed a weekend in which bombs killed more than two dozen people in Damascus and Aleppo. The government and opposition activists traded accusations over the attacks.
SANA said 27 people were killed when two "booby-trapped" cars exploded in Damascus on Saturday, and 140 people were wounded. On Monday, "the martyrs of the two terrorist blasts" in Damascus were buried, SANA reported.
A law enforcement member and a woman were killed in the Aleppo blast on Sunday, SANA said. An "armed terrorist group detonated a booby-trapped car while the authorities were dragging it out of a residential area," the report said.
A Syrian rebel leader over the weekend rejected the governments' claims.
"This is the regime's game. This is how they play their dirty tricks. They carry out these types of explosions from time to time to get more international support and compassion," Capt. Ammar al-Wawi of the rebel Free Syrian Army said Sunday. "They are desperately trying to prove to the world that they are fighting against armed gangs, but the reality is they are the ones who are doing all the killings."
A spokeswoman for European Union foreign policy chief Catherine Ashton issued a statement Monday condemning the blasts, saying, "There is no justification for the indiscriminate killing and maiming of innocent civilians, under any circumstances."
Ashton is also "following with great concern" the events of al-Mazzeh, the statement said. "These tragic events underline the urgency to stop the spiral of violence in Syria and to protect the lives of Syrian citizens."
Ashton called on Syrian authorities to cooperate fully with Annan.
Meanwhile, Syria's arms imports have increased almost six times from 2007 to 2011 compared with the previous five years, largely from Russia, according to a report published Monday by the Stockholm International Peace Research Institute.
Russia supplied 78% of Syria's imports between 2007 and 2011, the institute said. Russia continued delivering missile systems to Syria in 2011, it said, but the report did not indicate how many weapons were sent to the regime after the government crackdown started in March 2011.
The al-Assad family has ruled Syria for more than four decades and says it has popular support for its actions.
CNN's Saad Abedine, Amir Ahmed, Holly Yan, Chelsea J. Carter and Rima Maktabi contributed to this report.