Merkel and Cameron in battle over European Commission
Centre-right leaders from Sweden, Germany, Britain and the Netherlands are meeting near Stockholm to try to reach a consensus on European reform.
The controversial question of who is to head the European Commission is likely to be discussed, but not officially.
UK PM David Cameron is expected to try to get leaders on-side to block Jean-Claude Juncker taking the job.
It sets him against German Chancellor Angela Merkel, who publicly supports the ex-Luxembourg leader's appointment.
EU leaders have traditionally named the Commission head on their own, but new rules mean they now have to "take into account" the results of the European Parliament elections.
The European People's Party (EPP) - the largest centre-right grouping in the parliament, of which Mr Juncker is a member - won the highest number of seats in May's polls, and he has argued that gives him the mandate.
But observers say neither he nor any other candidate has managed to obtain a majority so far. Some EU leaders, including Mr Cameron, insist that the Commission's priorities need to be redefined first before an appropriate candidate is chosen.
Commission president is the most powerful job in Brussels, shaping EU policy in key areas such as economic reform, immigration and ties with other global powers.
Few details from the mini-summit in Harpsund have emerged. However, job creation, institutional changes in the EU and structural reforms to boost EU competitiveness were said to be high on the agenda.
The UK, Sweden and the Netherlands are leading a campaign to block Mr Juncker's candidacy, which has the support of the EPP.
Before the two-day talks began on Monday, Mr Cameron said he had the support of "all major UK parties" in opposing the appointment.
He also spoke to the prime ministers of Italy and Hungary, Matteo Renzi and Viktor Orban, by phone to discuss the matter, Reuters reports.
The BBC's Ben Wright in Harpsund said the scene was set for a lengthy power struggle between EU leaders and the European Parliament, with the UK worried about the prospect of a "stitch-up".
Mr Cameron is strongly opposed to Mr Juncker's belief in a closer political union between EU member states and has described Brussels as "too big" and "too bossy".
On arrival in Sweden, Mr Cameron said it should be EU leaders and not the European Parliament who decide who will head the commission.
Swedish Prime Minister Fredrik Reinfeldt also dismissed the idea of a stronger role for the European Parliament.
"We in principle dislike the idea of presenting front-runners from the different parties because we think that twists the balance between the institutions and the way that the Lisbon treaty is set up," he said.
More discussions were needed on the role of the EU commission before looking at names, he added.
Juncker: For and against
Angela Merkel: German chancellor, after some hesitation, backed European People's Party candidate. Some in Germany believe she may be willing to discuss alternatives
David Cameron: Opposed to former Luxembourg PM's candidacy - said to see him as a "face from the 1980s" who cannot solve the problems of next five years
Fredrik Reinfeldt: Seen as opposed to Mr Juncker and reports in European media suggest Swedish prime minister himself could be compromise candidate
Mark Rutte: Dutch PM opposed to Mr Juncker, due to meet Irish prime minister after Swedish summit to discuss alternative candidates
Dutch PM Mark Rutte told reporters that it was premature to put forward names for who should replace Jose Manuel Barroso as head of the commission.
"My belief is that we should first focus on content, discuss what the new commission should do... then discuss who fits that profile," he said.
Mrs Merkel said the four leaders would not make a final call on whom they would back, adding that her position was well known.
The decision will be made by the European Council - the official body comprising the 28 leaders - by qualified majority vote. That means no single country can veto the choice.
The result is due to be announced at an EU summit on 26-27 June, although an agreement by then is by no means guaranteed.