BRUSSELS—The European Union's executive proposed Thursday that EU countries should start sending migrants back to Greece from March in a bid to clamp down on asylum seekers moving north.

If approved, the measure—a signal of EU frustration with the way the Greek government has dealt with migrants—will put an end to a six-year exemption for Greece and increase pressure on Athens to speed up migrant returns to Turkey.

The commission said that Greece has made "significant progress" in improving its system for handling asylum seekers. The process had been deemed deficient by EU's top court in 2011. That ruling triggered a suspension of current EU rules, whereby the first EU country a migrant sets foot in is responsible for the asylum application. Since February, the commission has detailed how asylum conditions in Greece should be improved to allow returns to be resumed.

However, the commission said that "deficiencies in the Greek asylum system remain," especially in housing conditions for unaccompanied minors and in lengthy bureaucratic procedures. It proposed that transfers to Greece "should be resumed gradually, on the basis of individual assurances from the Greek authorities for each returnee, guaranteeing they will be received in dignity," a caveat aimed at avoiding any future negative court rulings.

Migration commissioner Dimitris Avramopoulos said that resuming returns will have a deterrent effect: "Asylum seekers need to know they can't relocate themselves and that if they do so they will be sent back."

The proposal comes after EU immigration officials on the ground found that as many as 13,000 people who registered in Greece's migrant camps are unaccounted for and could have slipped north into Europe.

About 500 migrants cross Greece's northern borders each week and continue their journey into Europe with the help of smugglers, according to the immigration officials and Greek officials. With people still landing on Greece's Aegean islands at a pace of about 400 a week, according to the Greek migration ministry, that means Greece is stretched in all directions.

Evidence from Germany, France and Belgium shows terrorists mingled with the refugee stream in 2015, increasing the pressure on governments to tighten border security and make sure that migrants are accounted for.

The commission also urged EU states to take more asylum seekers officially from Greece under a so-called relocation program agreed in 2015 and which has so far seen modest results.

By resuming transfers back to Greece, the commission will also increase pressure on Greek authorities to speed up returns of Syrian refugees to Turkey: Under an EU-Turkey deal signed in March, Syrian refugees are to be returned to Turkey.

So far, no Syrians have been deported to Turkey under the terms of the deal, though 83 have gone back voluntarily. All deportations are on hold awaiting resolution of a case that has been stuck since the summer in Greece's court system, in which Syrians are appealing for authorities to consider their asylum claims.

Nektaria Stamouli in Athens contributed to this article.

Write to Valentina Pop at valentina.pop@wsj.com

(END) Dow Jones Newswires

December 08, 2016 07:35 ET (12:35 GMT)