A further 975 migrants arrived in the Greek port of Piraeus from the Aegean islands of Lesbos and Chios on Saturday morning, the Greek Coastguard reported.
Another 54 migrants were expected to arrive from the island of Kos later in the afternoon.
The Greek government estimates that 32,000 migrants have been stranded in Greece after Balkan countries closed their borders, stopping them from proceeding along the so-called Balkan route to richer countries in northern and western Europe.
Heavy morning rains turned the makeshift camp at Idomeni on the Greek-Macedonian border into a mud bath, while temperatures were just 4 degrees Celsius. Humanitarian organizations estimate that some 13,000 migrants are trapped there.
Aid organizations are advising the migrants that there is better accommodation in reception camps to the south of the border, such as Nea Kavala, some 15 kilometres from Idomeni.
Most migrants are not taking this advice and are remaining by the border crossing, hoping that the Macedonian authorities will open the border fence if only briefly to allow some to pass, reporters on the ground said.