The European Union (EU) estimates that up to four million people may try to leave the country because of the Russian invasion.
The bloc has relaxed its rules on refugees and says its member states will welcome the refugees with “open arms”.
More than 62,000 people entered Hungary from Ukraine between Thursday and midnight on Saturday, the police headquarters of Szabolcs-Szatmár-Bereg County said on the police website on Sunday.
The police data show 19,978 entered Hungary across the Hungarian-Ukrainian border on Thursday, 19,618 on Friday and 23,140 on Saturday.
The number of people who crossed the border from Hungary into Ukraine was also higher than usual, reaching 5,452 on Thursday, 5,744 on Friday and 7,810 on Saturday, the data show.
The county HQ said the police are working at full capacity at all five border crossings between Hungary and Ukraine, ensuring entry to arrivals from Ukraine.
Nobody seeking refuge in Hungary is being turned away at the border, the police added.
Arrivals from Ukraine who aren’t being assisted by family or friends, or who have nowhere to go for material reasons, are being accompanied to shelters where they are getting accommodations and food, police.hu said.
Source: HUNGARY today
Which countries are Ukraine’s refugees fleeing to?
Refugees are crossing the borders to neighbouring countries to the west, such as Poland, Romania, Slovakia, Hungary and Moldova.
On Tuesday, the UN said that more than 830,000 people had entered these countries from Ukraine.
Poland has so far taken in over 453,000 refugees, according to the UN. The Polish government says a further 50,000 are arriving every day.
Poland is also preparing a medical train to transport wounded Ukrainians, and has drawn up a list of 1,230 hospitals to send them to.
More than one million Ukrainians have settled in Poland in recent years, especially since 2014, when Russia annexed Crimea
As for other countries, the UN says that so far:
- Hungary had taken 116,348
- Moldova 79,315
- Slovakia 67,000
- Romania 44,450
- Russia 42,900
- Belarus 341
69,600 people have moved on from these countries to others in Europe.
Refugees are being told they do not need documents to get into neighbouring countries, but should preferably have their internal or foreign travel passports, birth certificates of children travelling with them and medical documentation.
To get refugee status, they need to be Ukrainian citizens or people legally living in Ukraine, such as foreign students.
However, many people have been waiting for up to 60 hours to cross at border points into Poland, in freezing weather, in queues up to 15km (10 miles) long. Those entering Romania have been waiting for up to 20 hours.
Many have not been able to board trains taking them out of Ukrainian cities.
What help are countries providing?
In Poland and the other countries bordering Ukraine, refugees can stay in reception centres if they do not have friends or relatives to stay with. They are given food and medical care.
Hungary and Romania are giving out cash allowances for food and clothing. Children are being given places in local schools.
Countries used to have time limits on how long refugees could spend in reception centres, but most are saying they are likely to waive them and that Ukrainians can stay as long as they need to.
The Czech Republic has activated its Migration Wave Preparedness Plan. This will help refugees apply for a special type of visa through a simplified procedure in order to remain, if needed.
How many Ukrainians are internally displaced?
The UN estimates there are now at least 160,000 people in Ukraine who have fled the war and are displaced within their own country.
The EU believes that figure could climb to seven million, and that 18 million Ukrainians will be affected by the war.
What rights do the refugees have?
The EU is preparing to grant Ukrainians who flee the war a blanket right to stay and work throughout the 27 nations for up to three years, according to EU and French officials.
They would also receive social welfare and access to housing, medical treatment and schooling for children.
This is in line with the EU’s temporary protection directive for refugees, drawn up after the 1990s war in the Balkans, but never used until now.
The normal rules for refugees have been lifted to let Ukrainians settle where they want in the EU.