A refugee walks among tents at a makeshift camp for refugees and migrants at the port of Piraeus, Greece March 30, 2016. REUTERS/Alkis Konstantinidis

By Karolina Tagaris and Lefteris Karagiannopoulos

ATHENS (Reuters) - Migrant and refugee arrivals to Greece from Turkey rose sharply on Wednesday, just over a week after the European Union and Turkey struck an agreement intended to cut off the flow and as hundreds marched through central Athens to protest that deal.

The demonstrators included human rights activists, students and migrants from among the thousands stranded in Greece by recent border closures across the Balkans.

Greek authorities recorded 766 new arrivals between Tuesday morning and Wednesday morning, up from 192 the previous day. Most entered the country via the northeastern Aegean island of Lesbos.

Italy reported an even larger jump on Tuesday, when officials there said 1,350 people - mostly from Africa - were rescued from small boats taking a longer migration route across the Mediterranean as the weather warmed up.

The EU Commission said on Tuesday that flows from Turkey to Greek islands had reduced in the last week, with only 1,000 people arriving compared to an average of 2,000 a day in the last couple of months.

It was not clear why numbers had dropped, but the Aegean Sea had been hit with bad weather and gale force winds, making the journey from Turkey on small rubber boats even more dangerous than usual.

Under the deal in effect since March 20, migrants and refugees who arrive in Greece from Turkey will be subject to being sent back once they have been registered and their individual asylum claim processed.

Returns are due to begin from April 4, and for each Syrian returned from the Greek islands to Turkey, one will be sent the other way for direct resettlement in Europe. Human rights groups and some governments have expressed concerns about the legality of the scheme.

"We should be under no illusion that the EU-Turkey deal will bring an end to the refugee crisis," Jane Waterman, of aid group International Rescue Committee, said on Wednesday.

Following the Balkan border closure that preceded the Turkey deal, an estimated 51,000-plus refugees and migrants, among them Syrians, Afghans, Iraqis and others fleeing conflict in the Middle East and Asia, are currently stranded in Greece.

"OPEN THE BORDERS!"

Some were among the around 1,000 people who joined the march to parliament and the adjacent local offices of the European Commission late on Wednesday, a police official said. They pushed children along in strollers and chanted "open the borders!"

Others held up banners that read: "No borders, no nations, stop deportations" and "Abolish the racist EU-Turkey agreement."

"I am here to press Greece to make Macedonia open the borders," said 26-year-old Afghan Mohammad Ansari who has been in Greece for a month. "Why are we staying here? We should go."

Some of the protesters had taken the train to Athens from the nearby port of Piraeus, the country's biggest, where nearly 6,000 people remain stuck after having arrived there on ferries from Greek islands close to Turkey before the deal.

Scores have found shelter in passenger waiting lounges while hundreds more sleep in the open, either in flimsy tents or on blankets spread on the dock.

Queues for the few portable toilets are long, and scuffles have broken out in recent weeks over mobile phone chargers and food distribution.

International rights group Human Rights Watch has described conditions at the port, including basic hygiene, as "abysmal".

Among those stranded in Piraeus on Wednesday was Mariam El Musa, a 37-year-old teacher from Aleppo, Syria. "The problem here is the psychology of the people," she said.

"People are angry and depressed because the borders are closed, because it takes ages to have a meal and because we are dirty... We Syrians thought we would stay in Greece for only two or three days."

(editing by John Stonestreet)