Two hours later, the TV said troops captured IS' former stronghold of Hajar al-Aswad and broadcast images showing troops waving the Syrian national flag in the heavily destroyed neighbourhood.
Abdel Rahman said IS sleeper cells may remain in Yarmouk, however, and further military operations could lie ahead before the area is declared secure.
Fighting died down around midday on Saturday amid reports that an evacuation deal could be reached.
They were heading east towards Syria's Badiya, the vast stretch of desert where IS still holds tiny slivers of territory.
Yarmuk is one of the closest spots to central Damascus to have been controlled by IS and the deal brokered in recent days to secure IS's exit handed the government full control of the capital and its outskirts for the first time since 2012. A statement carried Monday by Russian news agencies says there were no casualties or damage at the base.
AFP's correspondent in Damascus saw black smoke emerging from the capital's southern skyline around that time.
The wider area of Yarmuk was also home to hundreds of thousands of Syrians. The Observatory said Daesh militants began burning their posts in Yarmouk and adjacent areas.
The evacuations from Yarmuk were shrouded in secrecy and took place under the cover of darkness with no media present.
Syrian soldiers in the Yarmouk camp on Monday.
Earlier in the day, SANA's reporter said that the Syrian Air Force raided terrorists' sites and fortified points in al-Hajar al-Aswad amid a collapse in the terrorists' ranks.
Iranian officials have pledged to remain in Syria despite calls by the United States, Israel, and others for it to remove its fighters.
Yarmouk began as a refugee camp for Palestinians who fled or were expelled from what is now Israel during the 1948 war.
Attacks by Syria's government, as well as rebel and militant infighting, have ravaged the district for years.
The area was once Syria's biggest Palestinian refugee camp, home to around 160,000 people.
More than 1,000 Islamist fighters and civilians left Qadam in March for opposition territory in northern Syria.
The assault had killed more than 250 pro-regime forces and another 233 IS fighters, according to the Observatory.
Mattar Ismael, a journalist from southern Damascus, told VOA that the execution of the deal started at midnight Sunday, adding that locals reported seeing a convoy of buses entering the area during the night.
"The new arrival of Daesh [IS] fighters to the Badia threatens the entire region", Said Saif, a media spokesman for the Forces of the Martyr Ahmad al-Bado Brigade, told Syria Direct. The origin of the blasts was not clear.