The offer was aimed at averting a partial freeze on EU membership negotiations.
But Erkki Tuomioja, the Finnish foreign minister, who received the offer in Helsinki on behalf of the EU said: "This is not a solution."
But he did stress that the offer was seen as a positive development.
"We are taking note of an opening from the Turkish side which is a positive indication."
Finland currently holds the EU presidency, and will host an EU leaders summit on December 14 and 15, where a final decision is to be made on whether to suspend talks with Ankara on key policy chapters.
Olli Rehn, the EU enlargement commissioner, told reporters in Helsinki that Turkey "has to adhere completely" to EU demands that it open "all ports to all EU members", including Cyprus, which Ankara refuses to recognise.
There was confusion surrounding Turkey's surprise offer, which caught the 25-nation bloc off guard, as EU diplomats in Brussels started deliberations on how to punish Turkey for its refusal to put into effect a 2005 customs union pact to Cyprus and nine other EU nations that joined in 2004.
The offer was quickly rejected by Cyprus and Greece.
In Nicosia, George Lilikas, the Cypriot foreign minister, said the proposal was part of a premeditated plan aimed at swaying public opinion.
He said: "It's a mockery of the European Union since it lacks any serious content."
Giorgos Koumoutsakos, a spokesman for the Greek foreign ministry, said Turkey was obliged to open all its ports as part of the customs agreement.
He described the Turkish proposal as vague and open to "multiple interpretations".
Greece called on the EU to send Ankara a "strong message" by suspending talks on more than the eight of 35 policy areas the European Commission has recommended freezing.
Ursula Plassnik, the Austrian foreign minister, called for membership negotiations with Turkey to be suspended for at least a year.
She was quoted as saying in an interview with the Austrian daily Oesterreich: "I think we need a negotiation pause, a suspension of negotiations with Turkey of at least a year."
However, Carl Bildt, the Swedish foreign minister, welcomed the offer as "constructive".
He said: "Whatever happens, the accession negotiations must continue."
Britain, Spain and Sweden have indicated that suspending parts of Turkey's membership negotiations was too harsh and would damage ties with Ankara.
But France, Cyprus and Greece are demanding a harder line against Turkey. They have blocked negotiations with Ankara since September in protest over the country's refusal to extend the customs union to Cyprus.Güncelleme Tarihi: 20 Eylül 2018, 18:16