"It seems that over the weekend the numbers (of arrivals in Greece) surged and then died down," Melissa Fleming, spokeswoman for the UN refugee agency said, pointing out that there were "30,000 refugees on the Greek islands right now."
More than 4,500 others were on the island of Kos, which has previously seen clashes between migrants and Greek police, who last month used heavy-handed tactics to control crowds.
Fleming told reporters that "a few thousand" migrants and refugees were arriving in Greece each day.
Tensions have therefore mounted on the border between Macedonia and Greece, with police deployed in an attempt to keep order.
Fleming said 7,000 people entered Macedonia from Greece yesterday.
A full 5,600 crossed into Macedonia last Thursday, which Flemming said last week was likely a daily record.