"The number of refugees and migrants arriving in Greece is accelerating dramatically and has now reached the 160,000 mark," UNHCR spokesman William Spindler was quoted as saying in briefing notes published on the agency's website.
According to UNHCR, as of August 14, as many as 158,456 migrants had arrived in Greece by sea in 2015. The number of those who have entered the country by land through the border with Turkey is estimated at over 1,700.
The agency said that the pace of arrivals has been increasing, with more refugees arriving in Greece in July that during the whole of 2014. The majority of those who arrived last week were from Syria, Afghanistan and Iraq.
"We are recommending Greek authorities to designate a single body to coordinate an emergency response and set up an adequate humanitarian assistance mechanism," the UNHCR briefing notes said.
The agency said it was working to support Greek authorities and called on European countries to also support Greece.
Last week, EU Commissioner for Migration Dimitris Avramopoulos said the bloc would provide Athens with $33 million once Greece set up a special authority to deal with refugee processing logistics.
Including the latest figures on Greece, the total number of refugees crossing the Mediterranean from south to north this year is estimated at some 264,500, according to the agency.