"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, according to AFP.
Fleming told reporters that "a few thousand" migrants and refugees were arriving in Greece each day.
Many of those who arrive in Greece seek to head north in hopes of resettling in wealthier European countries, especially Sweden and Greece.
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 Monday.
A full 5,600 crossed into Macedonia last Thursday, which Flemming said last week was likely a daily record.