The German government has been canvassing support for a senior political leader to gather views in European capitals on a new future for the continent in the wake of the Brexit vote, with the aim of completing the task before the 60th anniversary of the Treaty of Rome next March.

EU heads of state, reeling from the UK’s vote to leave the European Union, want to be seen to be responding to the Eurosceptic mood, and some want a new “vision for Europe” document that distils the conflicting thinking.

EU heads of government are due to gather in Bratislava for an informal summit on 16 September to discuss the fallout from Brexit, but mainly focused on how the EU will operate in the future, including what more it can do to reduce youth unemployment, straighten out the eurozone and strengthen security. In practice, the meeting may also see a first EU response to the election of a new Tory party leader, and the pace at which Brexit talks will take place. Those talks are to be led by a Belgian diplomat, Didier Seeuws, a former staffer for the former European council president Herman van Rompuy.

A cacophony of political voices have been setting out their plans for Europe, and some have called for a European convention to discuss ideas. Germany was strongly opposed and successfully saw off calls for a fresh convention last week. Berlin has, however, been looking at a more informal process in which a leading politician seeks to distil the mood in the capitals of Europe. There is a strong desire not to leave the process in the hands of either the commission president, Jean-Claude Juncker, and less so the council president, Donald Tusk.

In a sign that Germany wants to be at the helm of the discussions, Sigmar Gabriel, the economics minister and leader of the Social Democrats (SPD), has floated a series of ideas to change Europe, including fewer commissioners and a slimmed down agriculture budget. He said the EU could not afford to give the UK concessions or else “this will be an invitation to all the nationalist egotists in Europe”.

He also joined the German Greens in saying young UK citizens in France, Germany and Italy should be offered dual citizenship, as a way of keeping in touch with young Britons that back Europe. He was certain the UK had not left the EU for ever, saying: “I am sure this is an episode and not an epoch.”

But the efforts to refound Europe, or at least respond to its unpopularity, are made more complicated by a string of national democratic elections in Italy, Holland, France and Germany that could see a major change in tone in one or other of their capitals.

The Italian prime minister, Matteo Renzi, has said he will resign if his constitutional reforms to transform the country’s senate into a “senate of the regions” are rejected in a referendum that will be held by the end of October.

The pro-British Dutch prime minister, Mark Rutte, is trailing the anti-EU populist Geert Wilders in polls ahead of an election next March. The French presidential election, due next spring, may see the return of the mercurial Nicolas Sarkozy. He is producing a string of new ideas on the future of Europe, including reworking the governance of the eurozone so that it is dominated by France and Germany.

The German chancellor, Angela Merkel, currently facing a lot of the blame for Brexit, due to her rigidity on a range of issues, faces elections in the autumn.