"We have cleansed all the districts of Damascus, from Al-Midan to Mazzeh, from Al-Hajar Al-Aswad to Qadam... to Tadamun," the last rebel bastion in the capital, said the officer.
An anti-regime activist, Lena al-Shami, told AFP in Beirut by Skype that the rebel Free Syrian Army (FSA) had withdrawn from Tadaman and would focus on "hit-and-run tactics against important regime targets."
Tadamun borders the Palestinian refugee camp of Yarmuk and is home to both Syrians and Palestinians. It is now deserted and devastated, with electricity cables hanging down between rooftops and paving badly damaged.
In Yalda next to Tadamun, an AFP reporter saw a dozen corpses thrown on a rubbish dump. Some had been burned and others mutilated.
Fighting erupted in Damascus on July 15 and raged for several days as rebels seized several districts, forcing thousands of residents to flee.
In Aleppo, Abdel Jabar Oqaida, commander of the FSA there, said the Salaheddin district had "come under the heaviest bombardment since the battle began" on July 20 but that loyalists had "not managed to advance."
A senior government security figure warned that "the battle for Aleppo has not yet begun, and what is happening now is just the appetizer... The main course will come later."
The official said more reinforcements had arrived and that at least 20,000 troops were now on the ground. "The other side are also sending reinforcements," the official added of the rebels, who claim to have seized half the city.
Because of restrictions on the free movement of journalists in Syria, none of the claims can be verified.
-- July was deadliest month --
Echoing UN chief Ban Ki-moon's remarks on Thursday that violence was intensifying, a watchdog said July was the deadliest month since the uprising against President Bashar al-Assad's regime erupted in March 2011.
Rami Abdel Rahman who heads the Syrian Observatory for Human Rights said 4,239 people, the vast majority civilians, died last month, bringing the overall toll since March 2011 to more than 21,000.
Explosions shook Aleppo as fighter jets and helicopter gunships overflew the city and rebels tried to storm the state television building before being driven back by shelling, said the Britain-based Observatory.
State media said the army defended the site from "mercenary terrorist groups."
The violence killed at least 78 people across Syria on Saturday, including at least eight in Aleppo province, the Observatory said, listing the dead as 45 civilians, 26 regime forces and seven rebels.
On Friday, a day after UN and Arab League envoy Kofi Annan resigned in frustration over the failure of an April peace plan to take hold, Ban warned world powers they must overcome their rivalries to put an end to a "proxy war" in Syria.
And the UN General Assembly voted overwhelmingly to condemn the Security Council for its failure to act and condemned the Syrian regime for using heavy weapons.
Ban said growing radicalisation and extremism had been predicted at the start of the uprising, as had been a "proxy war, with regional and international players arming one side or the other."
After the General Assembly vote, US Ambassador Susan Rice said that "despite the continued opposition of an increasingly isolated minority, the overwhelming majority of UN members clearly stands resolutely with the Syrian people."
That was an allusion to Russia and China, who voted against the resolution and who had already vetoed three Security Council resolutions on Syria.
But Russian Ambassador Vitaly Churkin said the assembly gave "blatant" support to Syrian rebels and that its backers were the countries providing "mercenaries and arms" to the opposition.
China's deputy ambassador, Wang Min, said pressuring only Damascus would "cause further escalation of the turmoil and let the crisis spill over to other countries in the region."
On Saturday, senior foreign ministry official Wang Kejian accused countries that oppose its position of pursuing their own geopolitical interests and "trying to hinder or even undermine the political settlement process."
France's UN ambassador, Gerard Araud, said Paris would use its presidency of the Security Council to push for humanitarian aid for Syrians, warning Russian and Chinese intransigence could lead to "a final disaster."
While political progress "will be difficult," he said things can be done "on the humanitarian front because, above and beyond the deadlock on the Security Council or the resignation of Annan, there is the suffering of the Syrians."
In other developments on Saturday, Qatar said Arab states will not accept a replacement for Annan unless the nominee's mandate is to clearly negotiate a transfer of power in Syria.
And 48 Iranian pilgrims were kidnapped in Damascus, Tehran's consul said, while an official in Ankara said another Syrian general had defected to Turkey.