After a day of tense, last-minute negotiations, leaders of the 15 European Union countries reached agreement tonight to bring 10 more countries and 75 million more people into the organization, expanding its free-trade area for the first time across dismantled Cold War frontiers into former Communist countries of Eastern Europe.

"Today we have closed one of the bloodiest and darkest chapters in the history of Europe," said Danish Prime Minister Anders Fogh Rasmussen, the summit host, in announcing the agreement tonight. Posing for an official photograph with the leaders of the 25 current and incoming members, Rasmussen said, "Welcome to our family. Our new Europe is born."

The enlargement will create a trade bloc of 450 million people with an economy of $9.3 trillion per year, which would closely match that of the United States.

Tonight's celebratory mood was dampened by last-minute haggling by some of the invitees, notably Poland, which wanted more financial aid before closing the deal, and by lingering anger among Europeans at what was seen as heavy-handed lobbying by the White House on behalf an applicant not among the invited 10, Turkey.

The money dispute was resolved when the 15 current EU leaders agreed to give the Polish government more flexible use of funds it would be paid. The talks had become so tense that at one point, Rasmussen bluntly warned the Poles that no more money was available and threatened to allow the expansion to proceed without Poland. With 40 million people, Poland is by far the largest of the countries invited to join.

Under the final deal, current EU members will pay about $42 billion in farm subsidies and other payments to the incoming states over several years.

Plans call for the 10 to join in 2004, following a series of referendums, expanding the dream of a Europe without borders to a scale that was unthinkable just a dozen years ago. The newcomers will elect members to the European Parliament that year and later will likely adopt the European currency, the euro.

Membership is a risk for the EU, which is a rich man's club. The 10 new member states are, on the whole, poorer than existing members, have shorter histories as democracies, are more corrupt and have populations that are only lukewarm to the idea of joining the EU.

Three of the invited countries, Latvia, Lithuania and Estonia, were Soviet republics until just over a decade ago. Poland, Hungary, Slovenia, the Czech Republic and Slovakia were all communist-run.

"Our people surely deserve this chance for future generations," said Polish Prime Minister Leszek Miller. He thanked Pope John Paul II, a native of Poland, for strongly supporting the country's EU bid. He said the improved financial terms meant the government could more easily promote EU membership to Polish voters, who will be asked to ratify it in a referendum next spring. Many Poles feel they are being invited in as second-class citizens, because their farmers will get lower payments than counterparts in the current 15 countries.

The other two new members are the Mediterranean islands of Malta and Cyprus.

A hoped-for U.N. deal to end the 27-year division of Cyprus into zones for ethnic Greeks and ethnic Turks failed to materialize at the summit. But the EU invited the Cyprus government that it recognizes, which controls only the Greek portion of the island. The Turkish Republic of Northern Cyprus is recognized only by Turkey, and the people living there will not gain EU benefits unless there is a political reconciliation.

Talks about a deal were continuing. "We feel we are quite near" an agreement, said Cyprus's foreign minister, Ioannis Kasoulides. "With goodwill from both sides, we can conclude an agreement as soon as possible."

In another development at the summit, the EU reached an agreement with NATO that will allow a new EU military rapid reaction force to draw on certain NATO resources. That deal will allow the EU force to become operational by the middle of next year, officials here said, and function in a way that should complement NATO's own planned rapid response force.

The deal became possible after Turkey, a NATO member, dropped its long-standing veto over the use of NATO resources by the EU force. "EU access to NATO planning capabilities for EU-led operations is now assured, effective immediately," NATO Secretary General George Robertson announced in Brussels.

In response to Turkey's demand to start membership talks next year, the summit leaders resolved on Thursday that they would look again in December 2004 at Turkey's record on human rights, democracy and treatment of its Kurdish minority, and would start talks "without further delay" if EU standards in these and other fields are met.

The phrase "without further delay" was added tonight to assuage hurt feelings in Turkey.

In pressing its case, Turkey found a strong ally in the Bush administration, which has been trying to win Turkish support for possible war with Iraq. Bush intervened personally in recent days, telephoning Rasmussen and French President Jacques Chirac to plead Turkey's case.

But the U.S. lobbying created a backlash among some leaders, who were piqued at what they said was interference in an internal decision. "Do not underestimate the fury among the 15 EU members," said one senior European diplomat, who is normally friendly to the United States and asked not to be named. "It backfired extraordinarily."

"What the U.S. did was to raise Turkey's expectations to unreasonable levels," said this diplomat. "This is bigger than our differences [with the United States] over Iraq because the consequences can be disastrous. This could seriously affect the EU's relations with Turkey, and Turkey is our neighbor."

Others said the White House pressure campaign showed a striking lack of understanding about the EU's complex system of admitting new members, as well as an insensitivity to European domestic concerns. "It showed a misunderstanding of what the European Union is," said Daniel Keohane, a researcher at the Center for European Reform in London. U.S. officials "see it as a trade organization and nothing else."

Being a member of the EU, he said, "is a question of values, particularly democratic values and human rights. People didn't appreciate the U.S. stand that [admitting Turkey] is an important strategic objective."

Some European officials defended the U.S. effort. "I think it's entirely proper that the United States should be able to express its opinion along with everybody else," said Tom Kelly, spokesman for British Prime Minister Tony Blair.

Turkey's supporters in the EU, including Britain, painted the decision as a victory, because it gave Turkey a firm date for the first time, even if a further review was required before talks can start. "It's a huge demonstration of our confidence in the new Turkey that is taking shape and will eventually take its place in the family of the European Union," Blair said.

British Prime Minister Tony Blair, center, speaks to reporters after meeting with Turkish Prime Minister Abdullah Gul, left, and Recep Tayyip Erdogan, head of Turkey's ruling party.