Germany, already bearing the brunt of the human wave to Europe, said it could take half a million refugees annually for a few years, but stressed other European countries should accept their fair share.
With Greece's migration minister Yiannis Mouzalas admitting the island of Lesbos was "on the verge of explosion", authorities opened a new centre to process the 30,000 refugees the UN said are stuck there and on other Aegean Sea flashpoints, with Athens promising more for other bottlenecks.
Lesbos mayor Spyros Galinos said procedural pressures were easing after an additional 140 staff arrived from Athens to handle migrant and refugee registration.
"Some 7,000 people were registered yesterday and we expect at least the same number today," he told AFP.
Hours earlier, a handful of coastguards and riot police armed with batons had struggled to control some 2,500 migrants in Lesbos's main port, screaming "keep back" as the crowds surged towards a government-chartered ferry bound for Athens.
"I stayed here eight, nine days -- oh my God, I can't even remember," said Aleddin, an engineering student hoping to join his brother in Germany.
"Some people have been here for 14 or 15 days. The government doesn't care."
The chaotic scenes underscored the difficulty facing authorities across Europe as they struggle with waves of people trudging across the continent, many of them Syrians fleeing war and misery.
"The wave of migration is not a one-time incident but the beginning of a real exodus, which means that we will have to deal with this problem for many years to come," Tusk said in a speech at the Bruegel Institute, a think-tank in Brussels.