Most migrants then head north from Greece, but bottlenecks are forming in some Balkan states.
Slovenia has deployed its army to its border after being overwhelmed by numbers entering from Croatia.
The number of migrants reaching Europe has reached record levels in 2015:
The International Organisation for Migration (IOM) says more than 650,000 arrived so far this year, compared with 280,000 last year
The UNHCR says the number of migrants arriving by sea this month is already more than five times higher than the total for October last year
At least 3,135 have died making the journey - compared with 3,279 throughout 2014
Most travel from Turkey to Greece, and while summer months usually see the most arrivals, the number of people reaching Greece increased in October.
UNHCR spokeswoman Melissa Fleming said EU countries - who last month agreed to relocate 66,000 migrants from Italy and Greece - urgently needed to establish welcome centres as part of the deal.
"Obviously Greece is doing what it can, it`s pulling in additional police," she said.
"But we need to repeat over and over again that it is of utmost importance here that reception conditions be established and be adequate to this enormous task."
The relocation plan "is in serious peril and may fail", Ms Fleming said.
The UNHCR says only 19 migrants have been relocated in the last months - all Eritreans, who have moved from Italy to Sweden.
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Media captionGuy Delauney: "These are people just caught in politics between the countries"
Hungary closed its southern border with Croatia on Friday night, citing security concerns. The decision forced migrants to switch to a slower route via Slovenia.
Croatia and Slovenia imposed strict controls as a result, but those restrictions appeared to be relaxed on Monday night as many people waited in wet and windy conditions.
But Slovenia said it had been overwhelmed by the numbers entering from Croatia over the last three days.
Slovenia`s interior ministry says more than 19,500 migrants have arrived in the country since Friday, with at least 5,092 crossing the border on Tuesday alone.
It had previously said it would take in only 2,500 migrants a day.
Slovenia has called on European Union member states to help with the influx of migrants who have entered the country over the past few days.
Prime Minister Miro Cerar said the current numbers were beyond anything the small country could cope with.
"It is wrong to foster the illusion that it is possible for a small nation of two million people to stop, solve and rectify a situation where even much bigger EU member states have failed," he said.
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