The Syrian government has executed thousands of prisoners in mass hangings and carried out systematic torture at a military jail near Damascus, rights watchdog Amnesty International has said.

Amnesty said the executions took place between 2011 and 2015, but were probably still being carried out and amounted to war crimes. It called for a UN investigation.

Syria's government and President Bashar al-Assad have rejected similar reports in the past of torture and extrajudicial killings in a civil war that has claimed hundreds of thousands of lives.

The Amnesty report said an average of 20-50 people were hanged each week at the Sednaya military prison north of Damascus. Between 5,000 and 13,000 people were executed at Sednaya in the four years after Syria's popular uprising descended into civil war, it said.

"The victims are overwhelmingly civilians who are thought to oppose the government," the report said.

"Many other detainees at Sednaya Military Prison have been killed after being repeatedly tortured and systematically deprived of food, water, medicine and medical care."

The prisoners, who included former military personnel suspected of disloyalty and people involved in unrest, underwent sham trials before military courts and were sometimes forced to make confessions under torture, Amnesty said.

The executions were carried out secretly and those killed were buried at mass graves outside the capital, with families not informed of their fate, it said.

The report was based on interviews with 84 witnesses including former guards and officials, detainees, judges and lawyers, as well as experts on detention in Syria.

"The Syrian state's backers, in particular Russia, with its permanent seat on the Security Council, and Iran, must condemn the extrajudicial executions and extermination policies of the Syrian state and do what is in their power to bring them to an end," Amnesty said.