The president's remark came as he was speaking to students at the College of Europe at Natolin, Poland, during his trip to the European Union member state on Monday.
He said the EU with Turkey will be much more influential in the Balkans, the Mediterranean, the Black Sea, the Caucasus and the Middle East, adding that Turkey's accession to the EU will only help Europe find the role it deserves in this newly emerging global order.
He said Turkey has much to contribute to the EU so that it would not turn into what he warned earlier to be "an inward-looking organization" with its global influence and strategic outreach ending at the borders of its members.
The president said an EU including Turkey will be more successful in dealing with both external and internal threats to Europe's security, and whatever challenges Europe may face, Turkey is a partner.
He stressed that Turkey seeks to establish peace, stability and security in the Middle East and North Africa and to assist these countries in their transition to democracy.
Speaking about a tide of democratic protests rocking the Middle East, Gül said Turkey's modernization process reflects the ability of a predominantly Muslim society in embracing democracy, human rights, the rule of law and good governance.
"Therefore," he went on, "in addition to its credibility, Turkey is also becoming a source of inspiration of a vibrant democracy and free market economy in the region"
"We believe that Europe will never reach its full potential unless integration with Turkey materializes," Gül underlined.
Gül also warned the 27-nation bloc against ignoring this "strategic imperative" and trying to keep Turkey out of the European integration process and said this means missing the "broader geostrategic picture."
Turkish-Polish ties everlasting
Speaking about Turkish-Polish relations, Gül said the ties have always been based on strong bonds of friendship, mutual respect and a common vision of solidarity in difficult times.
President Gül also shared a brief historical note as testimony to the fact that Turks have never recognized the division or occupation of Poland.
Gül said at receptions held by Ottoman sultans for the “corps diplomatique,” the chief of protocol would always announce the ambassador of Poland, who was absent as Poland did not exist at the time, as “on his way!”
"This was a clear demonstration of the Ottoman policy of not accepting the destruction of the Polish state," Gül said.
Freedom of expression in Turkey
Responding to a question over freedom of the press in Turkey, Gül said his country had introduced far-reaching political reforms to comply with the EU's Copenhagen criteria, which he said included expanding freedom of the press.
"It is unacceptable to place Turkey, which has been taking political steps to comply with the Copenhagen criteria, among countries that put limitations on freedom of the press. A mistake is being made and it is done in a deliberate campaign," Gül said.
He said laws in Turkey guaranteed no one could be put behind bars just because of his or her opinions.