Syrian state media denied a deal was reached to evacuate fighters.
"Damascus and its surroundings and Damascus countryside and its villages are completely secure areas", the statement said, adding that the army would continue to fight "terrorism" across Syria.
A war-monitoring group said about 1,600 people, including hundreds of Islamic State gunmen, left the area Saturday and Sunday, heading toward the desert in the east of the country after a deal with the government.
The spokesman went on to say that within the framework of the first joint commission of the JCPOA, which is expected to be held without the United States presence in the coming days at Iran's request, Tehran and the remaining sides will only discuss the JCPOA and the issues related to the deal.
Assad's refusal to accept any weakening of his power shows he "does not want a political solution", said Yahya al-Aridi, a spokesman for the main Syrian opposition group.
However former Sunday Times journalist Hala Jaber countered that Putin did not refer to Iran or other Syrian allied forces: "Iran's presence is not viewed in the same league as that of the USA and as such is not negotiable nor will be used by Syria as an exchange commodity..."More news: Putin Met With Assad in Sochi - Kremlin Spokesman
In 2016, government forces enjoyed their biggest victory, capturing neighborhoods in Aleppo that rebels had controlled for years.
The official says the cease-fire ends at noon on Monday, after which government forces will resume their operations in the Hajar al-Aswad and the nearby Palestinian refugee camp of Yarmouk.
Both Russia and Iran have provided crucial military support to Assad's forces, giving them the upper hand in the civil war. "We will repel any aggression against Syria, regardless where it will take place", Riad Haddad told reporters in the Russian city of Sevastopol.
Iran will stay in Syria as long as it is needed, the Islamic Republic's Foreign Ministry Spokesman Bahram Ghasemi said.
Russian President Vladimir Putin told Assad during a meeting last week that a political settlement in Syria should encourage foreign countries to withdraw their troops from Syria.
In response, the Israeli Air Force conducted strikes against over 50 Iranian military targets in Syria and destroyed several Syrian air defense systems that had fired on Israeli jets, the army said.