Fully 6,037 people crossed into Hungary directly from Ukraine on Friday, while another 5,425 who crossed from Romania said they had come from Ukraine, the national police headquarters said.
Police issued temporary residence permits valid for 30 days to 638 people, the police website said on Saturday. Holders of such permits must contact a local immigration office near their place of residence within 30 days to apply for permanent documents, it added.
Budapest police received 1,364 refugees, 620 children among them, on Friday, according to the Budapest police website.
Refugees arriving on special train services at Kőbánya felső railway station, in eastern Budapest, were taken by bus to the BOK sports and events centre serving as a humanitarian transit point.
The authorities transported 106 people, including 70 children, to accommodation in the capital and outlying areas.
The police have contracted 31 Ukrainian interpreters, and they are working closely with staff of the disaster management authority, the immigration office, the Budapest metropolitan council, as well as numerous aid groups, the statement said.