Prime Minister Tony Blair says it is too early to say whether Britain will hold a referendum on the EU constitution after the French voted no.
He called for "time for reflection", saying France's rejection of the document raised profound questions about Europe's future.
Opposition MPs have called on Mr Blair to declare the treaty dead. Jack Straw will make a statement to MPs on 6 June.
Almost 55% of French people voted "No" and 45% "Yes".
The Dutch are also predicted to return a similar result when a referendum is held in Holland on Wednesday.
'Wait and see'
The UK is set to take over the presidency of the EU on 1 July. European leaders will meet on 16 June to see if the treaty can be salvaged.
Mr Blair, who is on holiday in Italy, insisted that if there was a constitutional treaty to vote upon "we will have a vote in Britain before ratifying it."
"What is important now is having a time for reflection with the Dutch referendum in a couple of days' time and the European council in the middle of June where the leaders will discuss the implications of the votes that have taken place," he added.
Mr Blair said the debate over the constitution, while sensible and necessary, did not reflect the concerns of ordinary people.
"The problem is there is another debate going on in Europe among the people of Europe which is to do with jobs, economic security, public services and welfare reform in an era of globalisation, illegal immigration, organised crime.
"Issues to do, in other words, with the economy and security that seem to them the issues they want to see leadership from Europe on."
He argued the constitution was a "perfectly sensible set of rules to govern Europe", but added that there was a "bigger debate now in Europe".
Foreign Secretary Jack Straw said he would be making a Commons statement on Monday on the implication of the French vote.
1 June - Dutch referendum on the constitution
6 June - Jack Straw makes Commons statement
16 June - Meeting of European leaders
1 July - UK takes over EU presidency
He suggested that he would say then whether the government would continue with its plans for a referendum on the constitution.
"It's a matter of judgment of my ministerial colleagues," he told BBC Radio 4's Today programme.
"But I think that would be one of the appropriate moments to make that clear."
He said the Dutch vote on Wednesday "will obviously be significant".
"If they vote no, we would have to take that into account. We would then have two of the six founder members of the EU coming to a decision," he told BBC News 24.
Shadow foreign secretary Liam Fox said it was time for the government to declare the treaty "dead".
"This treaty does not do what the people of Europe want and I think it should be put to rest right away," Dr Fox said.
Pro-European Tory former chancellor Kenneth Clarke said he was certain Britain would not have a referendum now.
He said he had always thought holding a referendum was an "unbelievably silly idea".
Shadow deregulation secretary John Redwood said he would support a referendum to ensure the EU could not introduce some of the treaty's measures "by the back door".
Liberal Democrat leader Charles Kennedy told BBC Radio 4's Today programme: "Without the acquiescence of the French, you can't really make meaningful progress on this constitution."
Other supporters and opponents of the treaty have been giving their reaction.
Lucy Powell, campaign director of Britain in Europe, called the result "very disappointing".
UKIP leader Roger Knapman said he was "very pleased" by the French "no", adding: "I think the constitution is now dead."
Scottish National leader Alex Salmond said it would be a sign of "arrogance" if Britain pressed ahead with a referendum.
The constitution aims to streamline decision-making in the enlarged EU of 25 countries. It has to be ratified by all member states to become law.