Syria's justice ministry has dismissed as "completely false" an Amnesty International report alleging up to 13,000 people were hanged over five years in a Syrian government prison.

The justice ministry said the Amnesty report was "completely untrue and intended to harm Syria's reputation in international forums," the official SANA news agency reported.

Amnesty said the alleged executions took place between 2011 and 2015, but were probably still being carried out and amounted to war crimes.

It called for a further investigation by the United Nations, which produced a report last year with similar accusations also based on extensive witness testimonies.

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 a 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.