The rebels fled the town south of Aleppo city after pro-government forces took full control, it said.
The Britain-based Syrian Observatory for Human Rights said Al Hader was the main bastion of rebels in the province’s rural south, where a major government assault backed by Lebanese Hezbollah fighters and Russian air strikes began last month.
Rami Abdulrahman, the head of the Observatory that tracks violence across the country, said the town’s capture would help the Syrian army press towards two besieged Shi’ite towns of Kefraya and al-Foua, further to the west in Idlib province.
Kefraya and al-Foua are part of a regional ceasefire deal that came into effect in late September and has largely held despite isolated violations.
The six-month deal includes the safe withdrawal of rebels from government-besieged Zabadani near the border with Lebanon, and the evacuation of civilians from the two Idlib villages.
The Aleppo offensive targets a large area to the south of the city, near the highway to Damascus, and is one of the major multiple assaults that the army has launched since the start of Russian aerial bombing in Syria aimed at bolstering President Bashar al Assad’s over-stretched forces.
The army and its allies, who have already captured several villages and towns, want to regain the initiative from rebels in the more than four-year-old civil war.
Rebels says the army’s next target was rebel-held Talaat al Eiss, only several kilometers (miles) west of Al Hader. Talaat al Eiss has also been under heavy army bombardment and Russian air attack since early this week.
Its capture would give government forces a big boost and allow them to disrupt rebel lines linking their Aleppo province strongholds with rebel-controlled Idlib.
“The heavy aerial bombardment of Al Hader and the surrounding area gave us no choice but to retreat, but these are to-and-fro battles, where we win ground one day and the next day we lose (it),” said Yousef al Issa, a field commander for Ahrar al Sham, one of the main insurgent groups fighting in the area.
Separately, aided by heavy Russian aerial bombing, the army fought its way into an air base elsewhere in Aleppo province on Tuesday, breaking a nearly two-year siege by Islamic State insurgents and freeing military personnel holed up inside.
Government forces have also retaken a few villages in the vicinity of the air base, expanding control over areas once controlled by the ultra-hardline jihadist Islamic State.