At the same time, regime troops supported by "reinforcements" geared up for a major assault on the former Yarmouk Palestinian refugee camp, 5 miles south of the center of Damascus, Syrian pro-regime newspaper al-Watan reported.
"Soldiers have massed in large numbers and are preparing a military operation to cleanse the camp," the newspaper said.
It didn't say when the operation would begin.
The Assad regime has vowed for months to "cleanse" greater Damascus of rebels.
Yarmouk Camp residents told al-Jazeera they saw no regime soldiers in Yarmouk late Tuesday but said mortar rounds had landed in several parts of the 0.8-square-mile neighborhood.
Gunfire echoed through the streets as fighting raged between rebel fighters and gunmen from a pro-Assad Palestinian nationalist organization known as the Popular Front for the Liberation of Palestine-General Command, the Qatari broadcaster said.
The rebel Free Syrian Army claimed Monday to have gained control of Yarmouk, a densely populated mixed neighborhood where more than 150,000 Palestinians live alongside 350,000 Syrians.
Tensions have increased in the neighborhood after regime airstrikes Sunday killed at least 25 people. Damascus has historically cast itself as a Palestinian champion and protector, but that has changed since the deadly airstrikes.
"No Palestinian will trust [the Assad regime] anymore after what they did on Sunday," Abu Khalil, a father of three who fled Yarmouk, taking refuge in Beirut's Sabra-Shatila refugee camp, told Britain's The Guardian newspaper.
Abu Khalil is one of more than 5,000 Palestinian residents who fled the violence in Yarmouk.
"All of us accept that blood has been drawn between us and the regime," Abu Khalil told the newspaper. "There is a debt to settle. It will never be like it was."
Sabra-Shatila is notorious for having been the site of a September 1982 massacre of up to 3,500 people, mainly Palestinian and Lebanese Shiite civilians, by a Lebanese Christian Phalangist militia assisted by Israel.
About 3,000 members of the Free Syria Army, the main Syrian armed opposition force, and the al-Qaida-aligned Jabhat al-Nusra, which Washington last week designated a terrorist group, are now inside Yarmouk, Abu Khalil said.
The FSA has been fighting the PFLP-GC, designated a terrorist organization by Washington, in an offensive to drive it from Yarmouk as rebel forces try to push deeper into the capital in a bid to topple the Assad regime.
Meanwhile, Russia Tuesday ordered warships to the eastern Mediterranean Sea, the Defense Ministry said.
An unidentified Russian naval official told the non-governmental Interfax news service the order was in preparation for a possible evacuation of Russian citizens from Syria.
The ships -- a destroyer, a tugboat, a tanker and two large landing vessels -- are "on their way to the coast of Syria for possible participation in the evacuation of Russian citizens" to a Russian port on the Black Sea, the official told Interfax.
The mission was planned swiftly and under total secrecy, the official said, adding the timeline for the ships' return to port depends "on the development of the situation in Syria."