NATO sent its ships into Greek and Turkish waters in the Aegean in March.
On Thursday, it said the number of migrants and refugees crossing the sea from Turkey was falling significantly, but smugglers can rapidly change routes and authorities must not reduce security efforts prematurely.
Speaking after a meeting with NATO Secretary-General Jens Stoltenberg in Athens, Tsipras said obstacles included not having full operational access in the region.
"Greece will undertake every effort so that NATO's mission contributes to the solution of the crisis," Tsipras said.
"Unfortunately it's clear that the obstacles .. arise from Turkey's unilateral demands and positions. Demands and positions which unfortunately are also expressed through a rise in activities which violate our airspace."
Europe signed an agreement with Turkey last month to close off the main route into Europe for more than a million people, most fleeing war and poverty in the Middle East, Asia and Africa.
"Our collective efforts are making a real difference. There's been a significant reduction in the number of people crossing the Aegean from Turkey to Greece," Stoltenberg said.
"We need to stay engaged."
