"Spain waited for seven years to join the EU. I do not want to talk about any definite date but we want to join the EU as soon as possible," Davutoglu said in exclusive interviews with Spanish "El Pais", "El Mundo" and "La Vanguardia" newspapers.
Davutoglu paid on Monday a formal visit to Spain, which will take over the rotating presidency of the union on January 1, 2010 for six months.
"This should not be perceived as if we would wait for seven years. We have already been waiting for half a century," he also said.
Davutoglu said that France and Germany had concerns about Turkey. Noting that France had concerns to prevent Spain's EU membership, Davutoglu said Madrid-Paris relations were better today than the past.
"We have a wide vision, and Ankara-Paris relations will be better when Turkey becomes an EU member," he said.
Also, Davutoglu referred to the Democratic Society Party (DTP) and with whom the government would negotiate its "democratic move" upon questions of reporters, and said there was a lawsuit at the Constitutional Court regarding the party, and the court was independent.
"(Abdullah) Ocalan was the leader of a terrorist organization and now he is in prison," he said.
Davutoglu defined the DTP as a political party represented at the Turkish parliament, and a legitimate party.
"We cannot negotiate with a terrorist, however we may do it with a legal party," he said.
Davutoglu said that the Turkish government wanted the broadest and best democratization in the long term.
"Turkish Constitution is naturally in the level of the EU, but it can be rehabilitated more because perfection is limitless," he said.
Davutoglu also said that the EU should keep its commitments to lift embargoes against the Turkish Republic of Northern Cyprus (TRNC).
Turkish Foreign Minister Davutoglu opened Turkey's Consulate General in Barcelona, was received by King Juan Carlos of Spain, and attended the Nueva Economia Forum on Monday.