The leaders of France and Germany want the eurozone countries to elect the president of a new "economic government" who would direct regular summits to respond to the continent's financial crisis.
The proposal fell short of what markets had hoped for: a grand plan to save the euro and, in particular, a sign the eurozone was moving toward a single bond issued by the 17 countries.
Global shares slid , as investors took little heart from the announcements.
French President Nicolas Sarkozy and German Chancellor Angela Merkel outlined their proposals in a letter to Herman Van Rompuy, president of the European Council. They said that they hoped Van Rompuy would get the job.
The two leaders, who met in Paris on Tuesday, called the twice-yearly summits "the cornerstone of the new economic government of the eurozone."
However, heads of the eurozone governments already hold summits, though not regularly scheduled ones, under the chairmanship of Van Rompuy. The first was in 2008.
Mr Sarkozy and Ms Merkel also raised the politically sensitive issue of pensions, saying eurozone states should rapidly implement structural reforms, including changes in "retirement policy."
As global stocks fell, shares in stock exchange operators were hit particularly hard on news the two leaders want to introduce a tax on financial transactions.