World Bulletin/News Desk
The informal meeting was held amid a high-profile campaign by Cameron, who has promised a referendum on Britain's continued membership of the European Union, to prevent the former Luxembourg prime minister being nominated to head the bloc's executive arm.
"I have said that for me Jean-Claude Juncker is the candidate for the office of Commission president and that I want to have him as the Commission president," Merkel told a news conference at the Swedish government's summer residence of Harpsund.
Britain regards Juncker as an old-style European federalist and says someone more open to reforming the EU and reducing the powers of Brussels should be picked, reflecting a widespread protest vote against the bloc last month.
Cameron had hoped the meeting could give more impetus to an alliance to block Juncker but a source in the British leader's office said discussions were "constructive but not resolved".
Playing for time, Reinfeldt and Rutte took no clear public position for or against Juncker, saying that the policy agenda for the next Commission had to be agreed first.
"We have agreed that the future policy priorities of the EU must be decided before we can decide on appointments of different top jobs," Reinfeldt said.
Juncker has the support of the European People's Party, the largest centre-right political grouping in the European Parliament, which named him as its candidate before last month's European elections.
Cameron has said EU leaders and not the European Parliament should nominate the candidate for Commission president, arguably the most powerful job in the bloc's institutions with major influence over policy affecting 500 million Europeans.
Leaders of the EU legislature have argued that the assembly should play a defining role in choosing the next Commission president, citing the bloc's governing Lisbon treaty which says the nominee should be chosen taking the elections into account.
EU leaders have mandated European Council President Herman Van Rompuy to propose a package of appointments for several top EU jobs, including the Commission presidency, if possible in time for a summit at the end of this month.
Under the Lisbon treaty, the decision is subject to qualified majority rule. Cameron appears to be short of a blocking minority unless Italian Prime Minister Matteo Renzi, who has said Juncker has no automatic right to the job, is willing to block the veteran Luxembourger.
However, Merkel, criticised by German media for her initial reticence in giving Juncker full-hearted support, has indicated she does not want to isolate Britain and would prefer a broad consensus if possible.