In a series of phone calls in recent days, he has spoken to six EU leaders, including German Chancellor Angela Merkel, Swedish Prime Minister Fredrik Reinfeldt and Hungarian Prime Minister Viktor Orban, and will make further calls on Tuesday, ahead of a post-election summit over dinner.
"Fellow leaders have agreed that it is an important moment for the European Council to set out its views on the future of the EU and provide clear direction of what is expected from the next European Commission," Cameron's spokesman said late on Monday in reference to the flurry of phone calls.
One of Cameron's immediate objectives is convincing other leaders that Jean-Claude Juncker, the former prime minister of Luxembourg, is not the right kind of person to lead the European Commission, with its sweeping legislative powers.
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Juncker, a long-time advocate of a more federal Europe, has been chosen by the EU's main center-right political group, the European People's Party, to be their candidate for Commission President, arguably Brussels' most powerful job.
With the EPP having won the most votes in the European elections, clinching 213 seats in the 751-seat European Parliament, Juncker is in pole position to secure the post, a point he firmly underlined on Monday.
But Cameron has concerns that Juncker, prime minister of Luxembourg for 19 years and at the heart of European politics for decades, is too much in the mode of old-school federalists rather than someone dynamic to lead change, EU officials say.
No commission names