Greece has been told it could face greater border controls, including temporary border closures, with Schengen zone states unless it fixes "serious deficiencies" in its own border management.
Greece, mired in a financial crisis, is on the forefront of Europe's migration crisis, but other EU states have grown increasingly critical of Athens' handling of the situation.
The European Commission said on Wednesday that Greece had "seriously neglected" its frontier duties to the Schengen zone, which allows for passport free travel between members.
A draft Commission report said Greece was failing to effectively identify or register migrants, or check travel documents against relevant databases.
Valdis Dombrovskis, the vice-president of the European Commission, warned that unless Athens took the "necessary action" member states could take measures, including temporarily closing their borders.
Since Greece has no land borders with the rest of the Schengen zone, that would mean installing new frontier checks at air and sea ports.
The next step in the process would be for Schengen member states - 26 countries, most of which are also in the EU - to confirm the findings of the Commission's report in a majority vote.
The executive would then recommend remedial measures and Greece would have about three months to implement them.
EU border agency Frontex has said its latest mission to the Greek island of Lesbos in January showed improvements in registration procedures.
Dombrovskis said the Commission acknowledged Athens was improving its handling of the situation, but there was still some way to go.
The vast majority of the more than one million migrants and refugees that arrived in Europe last year, came through Greece.
Yannis Mouzalas, Greece's migration minister, has warned that cutting off Greece from Schengen would cause a humanitarian crisis with thousands of people trapped in the country.