The Syrian Observatory for Human Rights said members of the Islamic Front coalition, dominated by the Ahrar al-Sham brigade and Al-Qaeda affiliate Al-Nusra Front, mounted the assault.
"Ahrar al-Sham and Al-Nusra Front have taken control of 80 percent of Aleppo central prison and freed hundreds of prisoners," Observatory director Rami Abdel Rahman told AFP.
But state television carried a breaking news alert, saying soldiers and security forces had "thwarted an attack against the prison by terrorist groups."
"Large numbers of rebels then followed by attacking the prison," he added.
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Ahrar al-Sham said opposition fighters had taken full control of the prison, as did the Aleppo Media Centre, a citizen-journalist outlet.
But Abdel Rahman said fighting was still ongoing at the complex, which reportedly holds some 3,000 detainees, including Islamists, activists and minors.
Rebels have launched attacks on the prisons for months, trying without success on several occasions to seize full control.
Conditions inside are said to be dire, with the Observatory reporting outbreaks of tuberculosis and other diseases.