“Irregular arrivals to Greece increased over the past weeks and months,” Avramopoulos told a news conference in Ankara, alongside the Turkish and German interior ministers.
“There is an urgent need to further strengthen the prevention and detection of irregular departures from Turkey,” he said.
The UN refugee agency (UNHCR) announced on Tuesday that arrivals by sea from Turkey to Greece, mostly of Afghan and Syrian families, increased to 10,258 in September.
That represented the highest monthly total since the 2016 deal between Turkey and the EU to curb the flow of arrivals, according to the refugee agency.
Turkish Interior Minister Suleyman Soylu however called on the EU to share the refugee burden as Ankara fears a new influx from Syria's Idlib province near the border.
Turkey “has fulfilled its commitments” under the 2016 accord with the EU, said Soylu.
“We expect Europe to be in the same frame.”
He also warned that the hostilities in Idlib could trigger a massive influx to Turkey, which is already home to 3.6 million Syrian refugees.
Avramopoulos said he appreciated the work already done by Ankara, “especially as the migratory pressure on Turkey continues.”
“Our joint visit is proof of our continued cooperation with Turkey on managing migration, together, as partners,” he said. Avramopoulos and German Interior Minister Horst Seehofer are due to visit Greece on Friday.
Seehofer said Europe was ready to help Turkey. “Wherever we can make a contribution we are willing to do so.”
The visit comes after Turkish President Recep Tayyip Erdogan threatened last month to “open the gates” to allow Syrian refugees to leave Turkey for Western countries if plans with the United States to establish a safe zone to resettle them in northern Syria fail.
“We will be forced to open the gates,” Erdogan said.
“We cannot be forced to handle the burden alone.”