"Turkey's EU membership would not only benefit itself, but it is also of vital importance for the peace and security of Europe," Yildirim told reporters ahead of a meeting with Greek President Prokopis Pavlopoulos in Athens.
Yildirim said Turkey did not only stop a "serious" refugee influx into Europe, stemming from the unrest and ongoing fighting in the Middle East, but also contributed "significantly" to the fight against terrorism.
"Therefore, we would like the European Union to appreciate this, and handle its relations with Turkey accordingly," he added.
Greece supports Turkey's European course, Pavlopoulos said, stressing that "we have always believed that Turkey must find its way to Europe".
"In order for a state to belong to the European Family, it must fully respect international law as a whole and, of course, the European acquis," the Greek President added.
Speaking on bilateral relations, Pavlopoulos said "there are more things that unite us than divide us," to which Yildirim responded by saying that the two countries shared the same geography, and consequently, the same destiny.
"With that awareness in mind, I think there is a lot we can do in every regard on the basis of good neighborly relations and respect for sovereignty," the Turkish premier added.
Yildirim arrived in Athens on Monday to attend meetings with Greek Prime Minister Alexis Tsipras, Pavlopoulos, and opposition leader Kyriakos Mitsotakis before departing for Komotini in northern Greece to attend an iftar, fast-breaking, dinner.