Clashes between migrants in an overcrowded camp at the port of Piraeus near Athens have left at least eight injured, officials say.
Afghans and Syrians are said to have taken part in the three-hour brawl there, where thousands of people live in filthy conditions.
On the island of Chios, migrants have broken out of a camp in protest.
Meanwhile, Greece is preparing to begin returning migrants to Turkey under an EU deal.
Lawmakers are expected to vote on a bill to facilitate the implementation of the agreement reached last month.
Under the deal, migrants who arrive in Greece from Turkey after 20 March are expected to be sent back if they do not apply for asylum or their claim is rejected.
The returns are set to start on Monday, but this has been under doubt as many of the support staff promised by other EU countries to help enforce the plan have still not arrived.
The deal has been heavily criticised by human rights groups, and the United Nations refugee agency has called for legal safeguards to be in place before any return takes place.
Five centres called hotspots have been set up to house and process migrants in Greece, but they are struggling to cope with the influx of people.
On the island of Chios, where one of these centres has been established, some 300 people, many of them women and children, tore down part of the razor wire fence and began walking to the port in protest, Reuters news agency said.
There are some 1,500 people said to be living at a site which has capacity for just 1,200.
Tensions were already high on Thursday night, when police used stun grenades as migrants staged a protest demanding to be allowed to leave the camp. Three people were taken to hospital.
Key points from EU-Turkey agreement
- Returns: All “irregular migrants” crossing from Turkey into Greece from 20 March will be sent back. Each arrival will be individually assessed by the Greek authorities.
- One-for-one: For each Syrian returned to Turkey, a Syrian migrant will be resettled in the EU. Priority will be given to those who have not tried to illegally enter the EU and the number is capped at 72,000.
- Visa restrictions: Turkish nationals should have access to the Schengen passport-free zone by June. This will not apply to non-Schengen countries like Britain.
- Financial aid: The EU is to speed up the allocation of €3bn ($3.3 bn; £2.3 bn) in aid to Turkey to help migrants.
- Turkey EU membership: Both sides agreed to “re-energise” Turkey’s bid to join the European bloc, with talks due by July.
Three people were also stabbed during rioting on the island of Samos.
Meanwhile, at the port of Piraeus, eight people were taken to hospital as clashes erupted between groups of migrants camping out there on Thursday. The fight left the area strewn with rocks and broken glass.
Most of the migrants there are from Syria, Iraq and Afghanistan, and for weeks they have slept in tents or blankets out in the open with poor sanitation and little food.
On Thursday, Greek officials started transferring some of those people to other accommodation elsewhere in the country. But some reportedly refused to leave, and about 5,300 were still there.
Frustration is mounting, Sarah Rainsford, BBC News, Lesbos
The UN refugee agency says detention should only be a last resort for asylum seekers, but every migrant who arrives here by boat is now taken to a closed camp. That includes women, children and the elderly.
On Lesbos, the facility being used is now overcrowded. Those inside say some people have to sleep in the open, and the UNHCR says food supplies are insufficient.
Frustration is clearly mounting as families, including those fleeing the violence in Syria and Iraq, now worry they will be sent back to Turkey.
But every day still brings boats loaded with new arrivals. They know their path through Europe may be blocked, but they are desperate enough to try to make it in any case.
The UN refugee agency has warned that conditions are worsening in Pireaus and also on the islands of Lesbos and Samos as well as at the Idomeni border crossing with Macedonia.
“The risk of panic and injury in these sites and others is real,” UNHCR spokeswoman Melissa Fleming said.
She urged the EU to provide greater support to boost Greece’s asylum system.
There are at least 51,000 migrants and refugees stranded in Greece after Balkan countries shut their borders last month, preventing them from continuing their journey to northern Europe.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
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