London objects to Merkel's favoured candidate to become the next European Commission chief, former Luxembourg premier Jean-Claude Juncker, on the grounds that he supports further political union in the 28-member bloc.
A spokesman for Cameron said he met Merkel at Britain's EU office in Brussels after a dinner for leaders of the Group of Seven industrialised nations.
"Their discussions focused on the next European Commission - the issues it should focus on and the appointment of the next president," the spokesman said.
"They had friendly, candid and constructive discussions in keeping with how their bilaterals usually are and in the spirit of finding consensus," the source said on condition of anonymity.
In diplomatic-speak, "candid" is often used to refer to an unusually frank exchange of views.
Cameron also spoke to Italian Prime Minister Matteo Renzi, EU President Herman Van Rompuy and outgoing European Commission chief Jose Manuel Barroso on the issue, Cameron's spokesman said.
EU leaders have traditionally named the Commission head on their own, but under new rules they now have to "take into account" the results of European parliamentary elections last month, though exactly what that means remains unclear.
Juncker, the former head of the Eurogroup of nations that use the single currency and prime minister of Luxembourg for 19 years, was the chosen candidate of the centre-right bloc that won most seats in the parliamentary elections.
Cameron is deeply wary of Juncker, an EU federalist, particularly after his party suffered a humiliating defeat to the eurosceptic UKIP party in last month's European elections.
Merkel slammed such arguments yesterday as "unacceptable."
Britain is believed to favour a candidate such as French IMF chief Christine Lagarde.
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