Luxembourg - currently holding the EU presidency - says ratification of the EU constitution will continue despite the French and Dutch "No" votes.
Luxembourg's Jean Asselborn denies EU constitution is dead
"We have to evaluate the message from the people to us... then I think we have to continue the ratification," Luxembourg's foreign minister said.
Jean Asselborn insisted that "we don't have a crisis".
French President Jacques Chirac and Germany's Chancellor Gerhard Schroeder will discuss the setback on Saturday.
Schroeder calls for calm
Mr Schroeder emerged from talks in Luxembourg on Thursday urging EU nations to continue ratifying the EU constitution.
The treaty must be put to all 25 member states, he said, adding: "Every form of over-reaction at this stage is wrong."
Luxembourg is due to hold a referendum on 10 July. Prime Minister Jean-Claude Juncker has said he will resign if his country rejects the constitution.
A recent opinion poll showed a surge in support for the "No" campaign in Luxembourg.
This week's "No" votes by two founding members - France and the Netherlands - could effectively kill the constitution, analysts say.
"We have a problem, but we cannot now say we stop everything," Mr Asselborn told the BBC's World Today programme.
"What is the alternative of those saying "No"? There is no alternative," he added.
European leaders will meet on 16-17 June for a summit that could decide the future of the constitution, drawn up over two years.
Latvia's parliament ratified the constitution by a vote of 71-5 on Thursday, bringing the number of countries backing it to 10.
ALREADY RATIFIED TREATY
The charter needs to be approved by all 25 states by the end of October next year in order to become law.
UK Foreign Secretary Jack Straw said the double rejection "now raises profound questions for all of us about the future direction of Europe".
Britain will take over the rotating presidency of the European Union next month.
The draft EU constitution was signed last year, after lengthy negotiations between member states.
It brings together for the first time the many treaties and agreements on which the EU is based. It defines the powers of the EU, stating where it can and cannot act and where the member states retain their right of veto.
It also defines the role of the EU institutions.