"There is no end date for NATO's activity in the Aegean sea... (but) NATO will continue to keep this mission under regular review," the official, who did not wish to be named, told AFP in Brussels.
The mission referred to was launched in February to tackle the huge flow of refugees and migrants to Greece on board rickety boats from Turkey.
Turkish Defence Minister Fikri Isik called yesterday for the mission's end because "there is no need for NATO forces in the Aegean".
He was speaking to reporters after a meeting in Brussels with defence ministers from NATO member states.
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"This was a temporary mission, and the goal has been reached... There is no reason to extend it," Isik was quoted as saying by the official news agency Anadolu.
Isik said Turkey would remain committed to tackling the flow of migrants and asked that the NATO mission be brought to an end "by the end of this year".
Asked whether the mission would continue in 2017, German Defence Minister Ursula von der Leyen said: "We'll see then."
Nearly a million people fleeing war, poverty and persecution arrived on the Greek islands last year in Europe's worst migrant crisis since World War II.
The number of arrivals in Greece has dropped dramatically this year, thanks to an EU-Turkey deal that went into force since March.
However, thousands of migrants have continued taking the more dangerous central Mediterranean route from Libya to Italy, over 5,000 of whom have died at sea.
"No decision has been taken on which nation will take up command of the group next," the official added.
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