Millions more in Syria could become refugees and head to Europe if there is no end to the war, Peter Salama, UNICEF's regional director for the Middle East and North Africa, has said.
"There could be millions and millions more refugees leaving Syria and ultimately (going) to the European Union and beyond," he said on Friday.
Salama also said that internal refugees in Syria has now reached almost eight million.
He issued the statement as Syrians and other refugees who are making their way to Europe, are facing several hurdles from police beatings to the bad weather.
At a railway station on Hungary's border with Austria on Friday, there was panic as Syrian refugees were crushed against barriers as they pleaded with the police for help.
In the Hungarian town of Roszke, where refugees are temporarily held, the wife of an Austrian politician has filmed the chaos as police threw food to refugees.
Michaela Spritzendorfer filmed the footage of the refugees surging forward against the fences surrounding them as officers toss food packets to them.
Record numbers of people, many of them fleeing war and conflict, continued to pour into Europe, with around 7,600 entering Macedonia in the last 24 hours.
It is inappropriate to talk about mandatory quotas, calculated on an extremely bureaucratic basis, almost like an accountancy exercise I might say, without consulting member states
Hungarian foreign minister says number of refugees in his country could rise to 400,000-500,000 by the end of this year.
Meanwhile, eastern European countries have rejected refugee quotas despite German warnings over the "biggest challenge" in EU history, amid disturbing footage of refugees in Hungary being fed "like animals".
German Foreign Minister Frank-Walter Steinmeier met counterparts from the Czech Republic, Hungary, Poland, and Slovakia in Prague, but failed to convince them to accept an EU plan to distribute 160,000 refugees around the continent.
"It is inappropriate to talk about mandatory quotas, calculated on an extremely bureaucratic basis, almost like an accountancy exercise I might say, without consulting member states," said Romania President Klaus Iohannis.
On Friday, the UN's refugee agency welcomed the EU plan to distribute refugees, but said more was needed to relieve pressure on frontline states.
"The relocation scheme can only succeed if it is accompanied by large-scale emergency reception, assistance and registration efforts in the countries most impacted by arrivals, particularly Greece, Hungary and Italy," said spokesman William Spindler, adding that 200,000 places would be needed by the end of 2016.
Hungary, which has been criticised for its anti-refugee stance, has sent more troops to help build a four-metre fence along its southern border with Serbia.
Despite laying razor wire along its 175-km frontier late last month, police said 3,601 migrants entered Hungary on Thursday, beating the previous record of 3,321 set two days earlier.
Macedonia is also contemplating building its own fence to stop the refugee influx, according to Foreign Minister Nikola Poposki, triggering a rush of refugees.
Related: Hungary holding refugees in closely guarded camps
On Thursday, Macedonian police trying to implement some order, beat back rain-soaked refugees as they attempted to enter the border from Greece.
Al Jazeera's Hoda Abdel Hamid, reporting from the border between Greece and Macedonia on Friday, said the situation has settled down after tensions on Thursday.
"The situation is calm and organised now," she said. "But they are very worried once they crossed into Macedonia."
Along with neighbouring Serbia, Macedonia has become a major transit country for tens of thousands of refugees who trudge up from Greece, after risking their lives crossing the Mediterranean Sea crammed into makeshift boats.
Meanwhile, a UNHCR spokesman welcomed an offer by US President Barack Obama to take 10,000 Syrian refugees but said it was inadequate given the scale of the exodus of people fleeing war and persecution.
The United States has taken in just 1,500 Syrians since the civil war began in 2011.
Source: Al Jazeera and agencies