Greece will not be able to start sending refugees back to Turkey from Sunday, the government said, as the country struggles to implement a key deal aimed at easing Europe’s migrant crisis.

Under the agreement clinched between Brussels and Anakara last week, migrants who reach the Greek islands will be deported back to Turkey. For every Syrian returned, the EU will resettle one from a Turkish refugee camp.

The deal aims to strangle the main route used by migrants travelling to the EU and discourage people smugglers, but it has faced criticism from rights groups and thousands took to the streets of Europe in protest.

Greek premier Alexis Tsipras told his ministers on Saturday afternoon to be ready to begin deporting people the following day, as agreed, but officials said afterwards they needed more time to prepare.

“The agreement to send back new arrivals on the islands should, according to the text, enter into force on March 20,” the government coordinator for migration policy spokesman Giorgos Kyritsis said.

“But a plan like this cannot be put in place in only 24 hours.”

Around 1,500 people crossed the Aegean to Greece’s islands on Friday before the deal was brought in, officials said – more than double the day before and compared with several hundred earlier in the week.

A four-month-old baby drowned when a migrant boat sank off the Turkish coast on Saturday, hours before the deal came into force, Turkey’s Anatolia agency reported.

Hundreds of security and legal experts – 2,300 according to Tsipras – are set to arrive in Greece to help enforce the deal, described as “Herculean” by European commission President, Jean-Claude Juncker.

Paris and Berlin have pledged to send 600 police and asylum experts to Greece, according to a joint letter seen by AFP.

But Greek officials said they were still waiting for the extra personnel and without them they would struggle to enforce the new accord.

“We still don’t know how the deal will be implemented in practice,” a police source on the Greek island of Lesbos told AFP.

“Above all, we are waiting for the staff Europe promised to be able to quickly process asylum applications – translators, lawyers, police officers – because we cannot do it alone.”

Realistically, migrants will likely not start being returned to Turkey until 4 April, according to German Chancellor Angela Merkel, a key backer of the scheme.

The numbers are daunting: officials said as of Saturday there were 47,500 migrants in Greece, including 8,200 on the islands and 10,500 massed at the Idomeni camp on the Macedonian border.

More than a million people entered Europe last year, many of them fleeing war and poverty in Syria, Afghanistan and other parts of the Middle East and Africa.

Around 4,000 people have drowned crossing the Aegean in flimsy boats, including 400 this year. Those already in Greece said they considered themselves fortunate.

“We were lucky to have arrived in time,” said Fatima, a Syrian woman at the port of Lesbos on Saturday.

She and her 13-year-old daughter were among some 2,500 people who boarded a ferry bound for Kavala in northern Greece, in a push by the government to move migrants to refugee centres on the mainland.

Another ferry was expected to leave from Chios island, Greek public television said.

“The authorities’ goal is to empty the islands,” where over 8,000 migrants are stuck, said Michele Telaro of the medical charity Médecins Sans Frontières (MSF).

Amnesty International has called the deal a “historic blow to human rights,” and on Saturday thousands of people marched in London, Athens, Barcelona, Vienna, Amsterdam and several Swiss cities in opposition to it.

“We’re calling on the Greek government to stop aligning itself with the EU’s anti-refugee policies,” said pro-migrant activist Thanassis Kourkoulas at a rally in the Greek capital.

EU officials have stressed that each application for asylum will be treated individually, with full rights of appeal and proper oversight.

In return for cooperation, Turkey won an acceleration of its long-stalled bid for EU membership, a doubling of refugee aid to 6bn euros ($6.8 billion) and visa-free travel in Europe’s Schengen passport-free zone.

The deal also envisages major aid for Greece, where tens of thousands of refugees are trapped in dire conditions after Balkan countries shut their borders.

At the squalid Idomeni border camp, refugees pondered reports of the new EU migrant deal.

Syrian refugee Yasmine said she will continue to wait at the Macedonian border with her two children and two sisters.

“They can’t prevent us from joining our husbands who were able to enter Germany this summer,” the former resident of Aleppo told AFP.