On the islands, the new arrivals have exacerbated an already combustible climate.
Lesbos hosts more than 19,000 refugees and migrants crammed into squalid conditions around a camp built to house less than 3,000, a legacy of the 2015 migration crisis.
Fed up with shouldering the burden of Europe's bloated asylum system, locals have protested against the presence of the migrants on their shores, because they threaten safety, public health and a tourism-dependent economy.
That anger has spilled over into violence in recent days, with an extremist minority accused of leading attacks on newly-arrived migrants, intimidating media and targeting aid workers, according to several groups based on Lesbos.
"Once night falls, there are non-stop attacks on NGOs, on workers, on people who are here as volunteers," said Douglas Herman, co-founder of the organisation Refocus, which teaches media skills to refugees.
"Most of those organisations right now have started to suspend their operations, some indefinitely.
Many have advised their staff to leave the island, and many have heeded that call," he told AFP, adding that all six of his group's current volunteers are departing.
The violence has been waged by "fascist" mobs, he said.
The Dutch group Boat Refugee Foundation, which provides medical care in Lesbos' Moria camp, said its staff and other aid workers were victims of such an assault by island residents on Sunday.
A spokesperson said the violence appeared to be led by a "small group of right-wing extremists" who want to prevent more refugees from coming.
The foundation's medical clinic has called a pause until it is deemed safe enough to continue, she added.
On Monday night, the crew of the human rights observation ship Mare Liberum said it was also "attacked by a mob of fascists" while docked on the island.
Police, who have been accused of a sluggish response, have opened an investigation after reports of several "attacks on people and cars" on Lesbos, a police source told AFP.
A day earlier officers fired tear gas at refugees who protested their detainment at the overflowing Moria camp.
After the recent surge of some 1,720 migrants to the Aegean islands in four days, the numbers slowed Tuesday as strong winds roiled the sea.
But confusion prevailed on Lesbos, where some migrants were boarded into vans for transfer only to be returned later to the beach where they had been camping.
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In the main city of Mytilini, police pushed back several hundred migrants who had gathered to reach the port because they heard a boat was leaving for the mainland.
Earlier, the island's MP Haralambos Athanasiou told AFP that all new arrivals would be "systematically sent to the mainland" and then back to their country.
In the meantime, not all aid groups are leaving.
"We don't plan to move," said the medical coordinator of Medecins du Monde, Dimitris Patestos.
There was "fear and insecurity" among some staff but so far the group had not encountered issues with locals, he added.