EU President Donald Tusk said Tuesday that excluding Greece from the bloc's passport-free Schengen zone would not be a solution to Europe's migrant crisis, as Athens comes under pressure to control the influx.

"Excluding Greece from Schengen solves none of our problems," Tusk, who is on a European tour, said on a visit to Greece after Athens announced that four of the country's five new registration centres were ready to receive migrants.