Syrian state TV reported the toll and showed footage of the blast scene in Damascus, including several damaged vehicles and a burnt-out car. The police officers' club was next to a vegetable market.
The Britain-based Syrian Observatory for Human Rights, an opposition group that tracks the civil war, said the blast killed eight policemen and wounded 20.
The IS group claimed the bombing in a statement circulated by its followers on Twitter, saying it was carried out by a fighter known as Abu Abdul-Rahman al-Shami. It vowed more attacks.
The Human Rights Watch report, released yesterday, said that cluster munitions, which are widely banned, have been used in at least 14 attacks across five provinces since Jan. 26.
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The attacks killed at least 37 civilians, including six women and nine children, and wounded dozens, HRW said.
Cluster bombs open in flight and scatter dozens of explosive munitions over wide areas. Some 98 States are party to a convention banning their use but several countries including Syria and Russia, as well as the US, China and Israel have not signed onto the ban.
Last week, Syrian troops and their allies were able to lift a three-year siege imposed on the Shiite villages of Nubul and Zahra in Aleppo province.
HRW said some of the recent attacks using cluster munitions occurred near the two villages.
Opposition activists have said that Russia has been using cluster bombs since the start of its aerial campaign in Syria on Sepember 30.