MEDYKA, POLAND/PRAGUE (REUTERS) - Eastern Europe's volunteer-driven aid effort to help Ukrainians was showing signs of strains of Friday (March 11), with some cities running out of accommodation as the number of refugees passed 2.5 million and fierce fighting continued unabated.

Relief work in frontline states - Poland, Slovakia, Romania, Hungary and Moldova - has mainly been shouldered by ordinary citizens volunteering to drive, cook or house refugees, with the help of non-governmental organisations and local authorities.

But with the war now in its third week and the number of refugees continuing to swell, it is becoming increasingly difficult to provide sufficient help.

In Krakow, Poland's second-largest city, one NGO described the situation at the city's train station as "tragic".

"There is nowhere to direct the refugees. They are stressed and confused, all kinds of help is needed, and above all, premises," tweeted Fundacja Brata Alberta, an NGO that in normal times helps individuals with mental disabilities.

"We call many places, but the only answer is: there are no more beds. Government intervention necessary!"

In Hrubieszow, a Polish town on the Ukrainian border, Mayor Marta Majewska said she had spent all the town's crisis reserve of 100,000 zlotys (S$31,300), as well as 170,000 zlotys from the local province, to run a refugee reception centre.

"I am most worried about electricity bills," she told Radio Zet. "The city cannot bear it at all."

Filling up fast

In Warsaw, the biggest temporary reception centre was about 70 per cent full by Thursday. Refugees now make up 10 per cent of the Polish capital's population, Mayor Rafal Trzaskowski said.

In Przemysl, near Poland's busiest border crossing that has become a transit hub for refugees, Vice-Mayor Boguslaw Swiezy said he was seeing a decline in the number of volunteers, some of whom are students, others people taking time off work.

The Polish government proposed a law this week allowing people who house refugees to claim 8.3 euros (S$12.43) per day per person.

It is also preparing a 1.6 billion euro fund to help refugees, and has mobilised police, firefighters and other services to distribute aid.

Romania's capital Bucharest was turning a convention centre and indoor arena, Romexpo, into its biggest refugee shelter yet, while Hungary was studying whether to turn museums, sports arenas and other public buildings in Budapest into shelters.

In the Czech Republic, Prague officials appealed to the general public and more hotels to receive refugees.

"The demand for accommodation in Prague is huge and is surpassing the offers available," Prague Mayor Zdenek Hrib said late on Thursday.

'I don't know what to do next'

And the refugees just keep arriving.

Dasha, a 31-year-old psychotherapist from Kyiv, arrived on Friday at Medyka, Poland's busiest border crossing with Ukraine, where temperatures overnight dropped to -9 deg C.

She left Kyiv on the first day of the invasion and stayed in the western city of Lviv but has now left Ukraine on the advice of her husband, who is in the army reserve.

"It's tough in Kyiv, they are encircling the city," she told Reuters, with two little dogs on their leashes.

"I'm going to Wroclaw (in south-west Poland), I have some friends there," she said before bursting into tears. "I don't know what to do next."

Inna, a 55-year old woman fleeing Dnipropetrovsk, said she had travelled 24 hours to reach Medyka.

"My town was bombed this morning... I just can't talk, I am so overwhelmed," she sobbed, adding she did not know where she would spend Friday night.

The United Nations bases its relief plans on 4 million refugees fleeing abroad, but has said it may need to revise the number higher.

The Polish Border Guard said 1.5 million people had entered Poland from Ukraine since Russia began its invasion on Feb 24.

Nearly 365,000 people have so far fled into Romania, 219,000 to Hungary and 176,000 to Slovakia, officials said. Nearly 200,000 have reached the Czech Republic, which does not share a border with Ukraine.

Russia calls its actions in Ukraine a special military operation to disarm its neighbour and dislodge its "neo-Nazi"leaders. Kyiv and its Western allies say this is a baseless pretext to invade a country of 44 million people.

Follow The Straits Times' live coverage on the Ukraine crisis here.