He was speaking after accusations of violence at the Greek-Turkish border.
Athens must respect international law amid the migrant crisis at its border with Greece, a senior EU figure has said.
Margaritis Schinas, vice-president of the European Commission, was speaking as migrants mass at the Greek-Turkey border.
Thousands have headed for the European Union after President Recep Tayyip Erdoğan said he could no longer stop refugees leaving Turkey.
But there have been reports of violence at the Greek-Turkish border.
On Wednesday, Turkey claimed a migrant was killed by gunfire while crossing into Greece. Greek officials strongly denied the accusation.
"Everything that is done at our external borders must be done in accordance with the law," said Greek politician Schinas.
He said he was "confident" that Athens could "even in these exceptional circumstances make their management of the situation compatible with the law".
Schinas also said Europe cannot fail twice on managing asylum and its borders, referring to the crisis in 2015 when around one million migrants made it to the EU.
"I dare say that this will be our last chance. Europe cannot fail twice on such an emblematic objective," he said, also calling for sufficient resources to be allocated to border controls in the next long-term EU budget, currently under discussion.
