Fully 4,596 people crossed into Hungary directly from Ukraine on Sunday, while another 6,826 from Ukraine crossed from Romania, the national police headquarters said.
Police issued temporary residence permits valid for thirty days to 679 people, the police website said on Monday. Holders of such permits must contact a local immigration office near their place of residence within thirty days to apply for permanent documents, it added.
Budapest police received 675 refugees, 251 children among them, by train, according to the municipal police website.
Meanwhile, the municipal government office of Budapest said staff at the BOK sports and events centre serving as a humanitarian transit point had helped 408 refugees on Sunday, accommodating 103 of whom stayed overnight.
The BOK centre provides food and drink, medical services, toilets, internet access and help with travel arrangements in cooperation with charity organisations and volunteers. National railways MÁV operates a ticket office at the site, while buses are provided to take people to the main train stations and the airport.