Fully 4,136 people crossed into Hungary directly from Ukraine on Saturday, while another 5,057 from Ukraine crossed from Romania, the national police headquarters said.
Police issued temporary residence permits valid for thirty days to 531 people, the police website said on Sunday. Holders of such permits must contact a local immigration office near their place of residence within thirty days to apply for permanent documents.
Budapest police received 539 refugees, 249 children among them, by train, according to the municipal police website.
Refugees arriving on special train services at Kobanya felso railway station, in eastern Budapest, were taken by bus to the BOK sports and events centre serving as a humanitarian transit point.
The Budapest government office said that 410 people received assistance at the BOK transit point on Saturday and 150 spent the night there.