The 18 EU countries that have approved the bloc's draft constitution have urged the nine other members to help revive the entire beleaguered document.
France and the Netherlands have rejected the constitution
Representatives of the states, meeting in Spain, called for the other nine members not to scrap the constitution but to help build on it.
The UK, Czech Republic and Poland want the constitution replaced by a new, slimmed-down mini-treaty.
French and Dutch voters rejected the constitution in referendums in 2005.
Spain's Foreign Minister Miguel Angel Moratinos told the meeting in Madrid the constitution was "a magnificent document" that should be "complemented rather than carved up".
"Is the only way out of the constitutional impasse the wholesale dismantling of the constitutional treaty? By cutting it into little pieces?" he asked.
The new constitution was drafted to streamline decision-making within the growing EU and would create a permanent president and foreign ministry.
The BBC's Oana Lungescu in Madrid says Spain now seems set on a collision course with opponents of the constitution.
Belgium and Luxembourg have expressed views similar to Spain's.
The German Chancellor, Angela Merkel, whose country holds the rotating EU presidency, aims to bring both camps together by June.
But our correspondent says that will not be easy.
Wary of dividing the EU even more, Germany only sent an observer to the Madrid meeting of "the friends of the constitution".
Germany did back the constitution in a parliamentary vote, but has not yet formally ratified it.
The countries represented in Madrid were: Austria, Belgium, Bulgaria, Cyprus, Estonia, Finland, Greece, Hungary, Italy, Latvia, Lithuania, Luxembourg, Malta, Romania, Slovakia, Slovenia and Spain.
Portugal also sent a representative, even though it has not ratified the constitution.
The conservative contender in the French presidential race, Nicolas Sarkozy, was the first to call for a mini-treaty that would be ratified by parliament, not through another referendum.
A mini-treaty would cut the existing constitution into bits and preserve only the technical changes that would allow the EU to work more effectively and admit further new members.
Mr Moratinos wants to enhance the existing constitution
The Europe ministers of Spain and Luxembourg, who organised the conference, say the countries that have approved the constitution - with a combined population of more than 270 million - want their voice to be heard.
In a joint article published in a number of European newspapers, Spain's Alberto Navarro and Luxembourg's Nicolas Schmit say that in today's globalised world "a united and capable Europe is more necessary than ever.
"We cannot resign ourselves to Europe being no more than a huge market or a free trade area," they write.