The draft Constitutional Treaty for Europe was "better" than the Nice Treaty agreed four years ago, according to the Polish Prime Minister, Mr Marek Belka.
Polish and Spanish objections were the main obstacles to an agreement on the text at last December's meeting of EU leaders.
But Mr Belka spoke in favourable terms about the results of the Brussels summit. "The important thing (for Poland) was to retain the weight of (the) Polish vote compared to that in Nice. We have succeeded in that," he said.
"The treaty as a whole is better than Nice. As far as Polish voting weight is concerned, it is slightly better, or at least as good as in Nice." Mr Belka complained, however, that Christianity was not explicitly mentioned in the preamble to the constitution.
Poland was the only country that to the end favoured a preamble to this effect. "We received no support from any other country," he said, adding that he had "no regrets" about the stance.
The Vatican also expressed regret that the new constitution does not mention Europe's Christian heritage. A Vatican spokes- man said the constitution had rejected "the historical evidence" of Europe's Christian identity. But he also noted "this new and important step in the process of European integration."
The religion issue led to an exchange between the French President, Mr Jacques Chirac, and the Italian Prime Minister, Mr Silvio Berlusconi, according to the Milan daily Corriere della Sera. It reported that when Mr Berlusconi raised the issue, Mr Chirac fixed him with a cold stare and said, "Thank you Father."
Turkey, a Muslim country that wants to join the EU, welcomed the omission of any reference to Christianity. "It is a constitution that we approve of," the Turkish Foreign Minister, Mr Abdullah Gul, told the Anatolia news agency. "There is no reference (to Christianity). It is a good constitution and it meets Turkey's expectations," he added.
The Russian foreign ministry welcomed the constitution as "an important step towards integration within the EU and the development of co-operation on the continent as a whole". A foreign ministry spokesman, Mr Alexander Yakovenko, said the Russian government believed the constitution would permit the EU to become "more transparent and democratic".
Meanwhile, Spain's conservative opposition accused the government of mishandling the talks. Mr Angel Acebes, deputy secretary-general of the Popular Party, said Spain "is no longer in the group of important countries".
However, according to the Hungarian Prime Minister, Mr Peter Medgyessy, a balanced constitution had been agreed, making the protection of national interests easier. He said it was important that with the compromise over the European constitution that came about in Brussels, the middle-sized countries, similar to Hungary, as well as the small ones, could advance their interests just the same as the big ones or ones with a large population.
In the Bulgarian capital, Sofia, the Ministry of Foreign Affairs welcomed the agreement as a "sensible and balanced" compromise that was, to a great extent, based on what was already agreed within the framework of the European Convention.
"The results achieved are the fruit of collective resolve and are beneficial to all present and future EU members and for Europe as a whole. This is a historical constitutional treaty . . . establishing preconditions for enhancing the role of the EU in international politics," it said.