The total number of migrants entering Austria from Hungary in the current wave is expected to reach up to 10,000, the Austrian interior ministry said Saturday.
Around 4,000 have poured across the border during the night and in the morning hours after Hungary began taking people in buses to the border.
The first bus carrying migrants who have been stranded in the Hungarian capital reached the Austrian border early Saturday, after Vienna and Berlin agreed to take in thousands of refugees desperate to start new lives in Western Europe.
Some 50 migrants from the 1,200 or so people who set off on foot from Budapest for the Austrian border earlier — including some in wheelchairs and on crutches — reached the Hegyeshalom-Nickelsdorf border post, Austrian police said, in the first of 100 vehicles laid on by the Hungarian authorities.
Several other buses earlier also left the Keleti train station in the Hungarian capital carrying people who have been stuck there for days in makeshift refugee camps waiting for trains to Austria and Germany.
Hungary has become the newest flashpoint as hundreds of thousands of migrants try to cross its borders on their journey to Western Europe, particularly Germany, which has said it will no longer deport Syrian refugees and will take in 800,000 people this year.
Berlin urged an end to “recriminations” as Britain said it would take in thousands more Syrian refugees — but only directly from camps, not those already in overstretched Hungary, Greece and Italy, who are demanding their EU partners do more to help.
The human cost of the crisis was exposed this week when the body of Syrian toddler Aylan Kurdi, which was buried with his brother and mother in his war-torn hometown of Kobane on Friday, was found washed up on a beach in Turkey.
On board one of the buses to Austria, exhausted migrants veered between concern and relief as they waited to see if their long journeys to Western Europe were about to come to an end. Many were nervous after Hungary tried to transport a trainload of migrants heading for Austria into a camp on Thursday.
“I was not comfortable leaving the Keleti railway station,” said 26-year-old Syrian Mohammed.
But he relaxed as he caught a glimpse of the Danube river through the window: “I had heard about it, but I’ve never seen it,” he said. “It’s beautiful.”
Between 800 and 3,000 migrants are expected to arrive at the Austrian border in the coming hours, said police spokesman Werner Fasching, adding that law enforcement and workers from the Red Cross were waiting to receive them.
Some 600 beds have been made available in Nickelsdorf for the new arrivals and neighbouring regions have also mobilised to ensure they are provided with food and medical care, he said.