BUDAPEST, Hungary (AP) — A fleet of Hungarian buses delivered more than 1,000 surprised and relieved migrants Saturday to the border of Austria, where charity workers offered the newcomers beds, hot tea and a warm welcome.

The pre-dawn move eased immediate pressure on Hungary, which has struggled to manage the flow of thousands of migrants arriving daily from non-EU member Serbia. But officials warned that the human tide south of Hungary was still rising, and more westward-bound travelers continued to arrive in Budapest within hours of the mass evacuation of the capital's central rail station.

Hungary relented in its demand for the travelers to report to government-run asylum centers when challenged by defiant migrants largely from Syria, Iraq and Afghanistan.

Thousands marched west Friday from the Keleti train station along Hungary's major motorway and camped overnight in the rain by the roadside. Hundreds more broke through police lines at a train station in the western town of Bicske, where police were trying to take them to a refugee camp, and blocked the main rail line as they, too, marched west.

Austria and Germany made the breakthrough possible by announcing Friday night they would take responsibility for the mass of humanity that was already on the move west or camped out in their thousands at Keleti. Hungary on Tuesday had suspended train services from that station to Austria and Germany, compounding the build-up of migrants there, in a futile bid to try to make the visitors file asylum papers in Hungary.

Austrian Federal Railways said the arriving migrants, once they passed through hastily assembled border shelters and refreshments, would be placed on trains to the capital, Vienna, and the city of Salzburg.

In jubilant scenes on the border, hundreds of migrants bearing blankets over their shoulders to provide cover from heavy rains walked off from buses and into Austria, where volunteers at a roadside Red Cross shelter offered them hot tea and handshakes of welcome. Many migrants collapsed in exhaustion on the floor, but with smiles on their faces.

The asylum-seekers in many cases have spent months in Turkish refugee camps, taken long journeys by boat, train and foot through Greece and the Balkans, then crawled under barbed wire on Hungary's southern frontier to a frosty welcome. While Austria, on Hungary's western border, says it will offer the newcomers asylum opportunities, most say they want to settle in Germany.

Since Tuesday morning, Hungarian authorities had refused to let them board trains to the west, and the migrants balked at going to processing centers, fearing they would face deportation or indefinite detention in Hungary. Government officials said they changed course because Hungary's systems were becoming overwhelmed by the sheer numbers of unwanted visitors.

Janos Lazar, chief of staff to Hungary's prime minister, said the migrants' surprise movements Friday were imperiling rail services and causing massive traffic jams. "Transportation safety can't be put at risk," he said.