Yildirim said that "the Aegean should be a sea of friendship between Greece" following a phone conversation with Greek premier Alexis Tsipras.
According to Greek news agency AMNA, a Turkish patrol boat rammed into a Greek Coast Guard patrol boat near the Kardak islets in the southeastern Aegean on Monday.
In Brussels, Greek defence minister Panos Kammenos said he had briefed USA defence secretary Jim Mattis and North Atlantic Treaty Organisation chief Jens Stoltenberg. The Greek boat, which was financed with European funds "to monitor Greek seas and European borders", suffered damage, the navy said.
Grigoris Demestichas, a retired Greek admiral, said: "This..."
"I had the opportunity to show them material of proof that dismisses Turkish claims that [the incident at Imia] was an accident", Mr Kammenos said in a statement.
Coastguard officers warned Kammenos, who was heading to the Kardak islets in an assault boat to lay a wreath there.
"H stressed the need to immediately put an end to the growing provocative Turkish violations of the Greek islands΄ territorial waters and the airspace in the Aegean and to reduce tension".
The U.S. officials will be joined by several more of their regional counterparts, according to a U.S. Embassy press release in order to discuss an array of topics that do not include the tense relations between Greece and neighbouring North Atlantic Treaty Organisation ally Turkey.
Turkey and Greece, Nato allies, have always been at odds over issues from ethnically split Cyprus to airspace and overflight rights and relations have worsened since Greece blocked the extradition of eight Turkish soldiers that Ankara accuses of involvement in 2016's failed coup.
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