EU countries have become increasingly critical of Greece's lax control of its border with Turkey, as the number of immigrants crossing it has risen due to political unrest in the Middle East.
A group of seven EU ministers of justice and home affairs urged Greece to improve border controls using available EU funds.
"The question still remains what happens when a country is not capable of securing its borders, as we see in Greece," German Justice Minister Hans-Peter Friedrich told journalists after a gathering of EU ministers.
"Is it possible to reinstate border controls?" he said. "I want to clarify that this is still part of our discussion."
His remarks were echoed by Austrian home affairs minister Johanna Mikl-Leitner. "We need to put political pressure on Greece to implement their asylum authority as rapidly as possible. This border is as open as a barn door."
Several EU governments have lobbied to make it easier to curb unrestricted travel in Europe and reinstate passport controls, abolished under the Schengen agreement.
Both ministers said Greece had done little to beef up its asylum agency. There was no immediate comment from the Greek government.
The European Commission has earmarked around €300 million in total for Greece to manage immigration. Athens has so far received more than two-thirds of this money.
The Greek government has said it plans to build a fence to stop illegal immigrants but Mikl-Leitner dismissed the idea, saying "fences were a thing of the past."
The bloc's border agency Frontex has said Italy passed Greece as the main point of entry into the EU for illegal border migrants in the first quarter of 2011, as unrest across North Africa prompted a wave of emigration.
France and Italy in particular have campaigned for more leeway on border controls. Many of the 20,000 refugees that landed in Italy from a civil war in Libya later travelled to France.