BRUSSELS, Belgium (AP) – The European Union and Turkey reached a historic agreement Friday to begin talks next year aimed at bringing the populous Muslim nation into the EU after hammering out a compromise over Ankara’s relationship with Cyprus.

Turkey accepted an offer from the 25 EU leaders during their two-day summit to begin talks on Oct. 3, 2005, launching a process that could take years and could transform the political and social landscape of both parties.

If the talks succeed, Turkey would become the largest EU member, with a population of 71 million – expected to grow as high as 85 million by 2020. But its per capita income is roughly one-third of the average of longtime EU member states, requiring far-reaching economic reforms.

Turkish membership would also add millions of citizens to the EU at a time when many Europeans are questioning whether their countries, which have Christian heritage, can absorb large numbers of Muslim immigrants.

Nevertheless, EU leaders hailed the agreement as a historic step, which would expand the borders of the EU from Ireland to Iran.

“If I think back on today, I believe we can say that we have been writing history today, and the agreement we reached today will acquire full significance in the years ahead,” said Dutch Prime Minister Jan Peter Balkenende, whose country holds the EU presidency.

British Prime Minister Tony Blair said the decision to accept Turkish membership shows “that those who believe there is a fundamental clash of civilizations between Christians and Muslims are actually wrong; that they can work together; that we can cooperate together.”

During the summit, EU leaders also agreed to start entry talks with Croatia next March if it hands over an indicted war crimes suspect to the international tribunal in The Hague.

The leaders also formally closed membership talks with Romania and Bulgaria, paving the way for them to join in 2007.

But the main attention fell on Turkey. Despite widespread public misgivings about Turkish membership, the leaders agreed Thursday to offer Ankara accession talks.

But the deal nearly fell apart because of an EU requirement that Turkey initial an agreement Friday expanding its customs union with the EU to include Cyprus and nine other members that joined in May. The agreement would have to be signed by October.

Turkish Prime Minister Recep Tayyip Erdogan balked at the requirement, which EU diplomats said amounted to tactic recognition of the Greek Cypriot government.

Turkey invaded Cyprus in 1974 to block a coup by Greek Cypriots, and decades of diplomacy have failed to reunite the Mediterranean island.

About 40,000 Turkish troops remain in northern Cyprus, which is controlled by Turkish Cypriots.

After hours of intensive negotiations, the EU agreed to accept a statement from Erdogan that he would sign the customs agreement before the talks start and that the move would not constitute recognition of Cyprus.

“This is a win-win agreement,” Erdogan said. “We’re at a point where we reaping the reward of 41 years of work. The process from now on will be even more difficult … but I strongly believe Turkey will be able to achieve this.”

EU officials said the talks would be open-ended and without a guarantee of eventual EU membership.

Nevertheless, the admission of Turkey to the EU is still strongly opposed in several EU countries, whose citizens fear an influx of culturally different migrants who would compete for jobs.

French President Jacques Chirac, who has promised a referendum on Turkish membership if the talks succeed, said the Turks would have to it would have to accept the mass killings of Armenians in the early 20th century.

Austrian Chancellor Wolfgang Schuessel said he would also call a referendum because bringing a Muslim country into the EU “must not be decided in an ivory tower … We cannot be indifferent about public opinion.”

Supporters of Turkey’s entry maintain that the country could be a bridge between Europe and the Middle East and stand as an example of a democratic state with Islamic traditions. Turkey, a longtime NATO member, has been legally secular since the collapse of the Ottoman Empire after World War I.