The push came a month after insurgents captured several military academies south of Aleppo and opened a corridor into rebel-held parts of Syria's largest city and onetime commercial centre.
Since then, government forces and their allies have been trying to recapture the area.
State news agency SANA quoted an unnamed military official as saying that troops have captured the Armament Academy and are "continuing their advance in the area to impose almost a total siege on the gunmen in Aleppo."
Al-Manar TV, which is run by Lebanon's Hezbollah group, said troops are now pushing toward the nearby Artillery Academy. Hezbollah has sent thousands of fighters to Syria to bolster President Bashar Assad's forces.
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To the north of Aleppo, fighting between Turkish-backed rebels and the Islamic State group intensified Sunday near the rebel-held town of al-Rai, near the Turkish border.
Turkey sent tanks into al-Rai yesterday in what it said was a "new phase" in an operation to drive IS away from the border. Al-Rai is 55 kilometers west of Jarablus, a border town seized by Turkey-backed Syrian rebels last week. The Turkey-backed forces are now advancing toward each other from both towns, hoping to close off the last stretch of the Syrian border ruled by the extremists.
The Observatory and the Local Coordination Committees, another Syrian monitoring group, said an IS suicide attacker riding a motorcycle struck in the northern village of Khalfatli, killing and wounding a number of people, including rebels. The Observatory said the blast killed 14 people, including 11 rebels.
The LCC said Turkish-backed Free Syrian Army rebels captured the village of Tweiran, to the south of al-Rai, from IS on Sunday. Turkey's state-run Anadolu news agency said 19 Syrian rebels wounded in clashes with IS since Saturday have been hospitalized in Turkey.
"We are there to protect our borders, ensure the safety of our citizens' lives and property, and to protect the territorial integrity of Syria," Yildirim said during a visit to the southeastern city of Diyarbakir.