UK prime minister Tony Blair has said Turkish membership of the EU is important for European security.
Mr Blair is a strong supporter of Turkey joining the EU
Speaking after talks in London with Turkish premier Recep Tayyip Erdogan, Mr Blair said he hoped accession negotiations would open on 3 October.
Both leaders agreed that Islamic extremists were trying to drive a wedge between the West and the Muslim world.
Mr Blair said terrorists must not be allowed to divide people by nation, race or religion.
The UK premier said the prospect of joining the EU - still at least 10 years away - had led Turkey to reform itself.
"I know there are many uncertainties in Europe at the present time, but the prospect of Turkish membership, though obviously some time in the future, I think will be important for Europe and for its security," he said.
"I would like to congratulate the Turkish government and the prime minister for the great changes that have been made in Turkey in the past two to three years as a result of the focus on membership of the European Union."
Mr Erdogan said he wanted to see "co-operation between civilisations" and he repeated a message of condolence for the families of those killed in the London bombings on 7 July.
On Tuesday Mr Blair held talks with President Tassos Papadopoulos of Cyprus.
The island's division remains a stumbling block to Turkey joining the European Union.
Mr Blair said: "We want to see unification take place and one of the things we have got to try to explore [during the UK presidency of the EU] is how we find the right way forward on that."
At a joint news conference with the UK prime minister Mr Erdogan said Turkey would not recognise Cyprus until there was a comprehensive peace settlement there.
His country is due to sign an agreement expanding its customs union with the EU to the 10 new member states, including Cyprus.
Signing it is the last hurdle Turkey must clear before accession talks begin.
Mr Blair said signing the Ankara protocol did not mean Turkey had recognised Cyprus.