In a joint press conference with Swedish PM Fredrik Reinfeldt, Mr Cameron said they saw the issue as a “shared priority”.
Sweden will be among the countries attending a Nordic-Baltic summit in London next year to exchange ideas.
Economic recovery, the EU Budget and Afghanistan were also on the agenda as the two leaders met at Number 10.
They said they were agreed on the need for the EU to scale back next year’s budget in the light of austerity measures being imposed by governments across Europe, and both backed the EU/IMF loan to Ireland.
Following the press conference, Mr Cameron and Mr Reinfeldt visited The Royal London Hospital, which is being rebuilt by Swedish company Skanska, and met British and Swedish staff employed on the site.