The German and French leaders have urged EU nations to continue ratifying the constitution despite the "No" votes in France and the Netherlands.
The mood was probably more sombre at the Berlin dinner
Chancellor Gerhard Schroeder and President Jacques Chirac voiced their position after meeting in Berlin.
Meanwhile, European Commission President Jose Manuel Barroso has said the bloc must not fall into paralysis despite the setbacks.
He urged EU leaders to "turn a crisis into an opportunity".
German government spokesman Bela Anda said that the chancellor and President Chirac "were in agreement that the constitutional process must continue so that the views of each country are respected".
"We cannot drop the idea of Europe because there are difficulties," he added, the Associated Press news agency reported.
Meanwhile, his French counterpart Jerome Bonnafont said the talks "demonstrated a profound unity of views on what has happened in Europe and what must happen going forward".
The two men are due to meet again on 10 June. Mr Schroeder will then meet with UK Prime Minister Tony Blair in Berlin on 13 June.
Mr Chirac may have felt a tinge of envy when he sat down for the dinner, the BBC's Ray Furlong in Berlin says.
Mr Schroeder got the EU constitution ratified in parliament almost unanimously, avoiding the mess that a referendum might have caused.
The two leaders know there is considerable scepticism about the ratification process continuing and are particularly concerned that Britain might declare the constitution dead before the EU summit in mid-June, our correspondent says.
The UK Foreign Secretary Jack Straw is expected to tell MPs in London on Monday that the government is shelving plans for a referendum on the EU constitution.
The two European leaders also discussed the EU budget covering 2007-2013.
Germany, the biggest contributor to EU funds, wants Britain to make concessions over the budget rebate won by Margaret Thatcher in 1984.
But this would be politically explosive in the UK, our correspondent says.
Speaking in Messina, Italy, earlier on Saturday, Mr Barroso said: "It is vital that we use the present moment to forge a new consensus."
"What we need now is an intelligent synthesis between the market and the state which can help Europe win and not lose in the face of globalisation," he said.
"It is the role of the Commission... to avoid a confrontation between the different models or perceptions in Europe."
Mr Barroso was apparently referring to the French referendum on the EU constitution, which revealed local fears that Europe may be increasingly turning to the "Anglo-Saxon" liberal economic model.
However, Mr Barroso added that he "cannot see how to reopen negotiations with a view to revising the constitution".
"Its text represents a very delicate compromise which took several years to work out," he said.