Refugees call for a no-fly zone over Ukraine - something NATO powers have so far ruled out on the grounds it would risk escalating the conflict beyond Ukraine.
Ukrainians fleeing into central Europe have urged Western nations to take tougher steps against Russia following Moscow's invasion that has created more than one million refugees.
At the Medyka crossing, Poland's busiest, along its roughly 500-kilometre border with Ukraine, refugees called for a no-fly zone over Ukraine - something NATO powers have so far ruled out on the grounds it would risk escalating the conflict beyond Ukraine.
"Please close the sky," said Solomiya Zdryko, 18, who fled from Lviv in western Ukraine.
"I know that it's not possible for us to join NATO but at least close the sky because people are dying."
"It's great that the whole world is watching us and supporting us, but it really needs to stop," she added.
With Russian forces stepping up their attacks on Ukrainian cities, some refugees said that while they were grateful for the support they were getting, they wanted foreign powers to do more.
"They could do more only by closing the skies," said a 33-year-old woman who arrived from Lviv and who gave her name only as Olha.
Russia said its forces had stopped firing near two besieged Ukrainian cities on Saturday to allow safe passage to civilians fleeing fighting, but officials in one of the cities said Moscow was not fully observing the limited ceasefire.
READ MORE: Ukraine refugees: where are they fleeing to?
'Fastest moving' refugee crisis
The number of refugees could potentially rise to 1.5 million by the end of the weekend from a current 1.3 million, according to the head of the UN refugee agency, Filippo Grandi.
"This is the fastest moving refugee crisis we have seen in Europe since the end of World War Two," Grandi said.
Most escaping Ukrainians have crossed into the European Union in eastern Poland, Slovakia, and Hungary and northern Romania.
Poland, whose Ukrainian community of around 1 million is the region's largest, has accepted nearly 800,000 Ukrainian refugees since the start of the Russian invasion on February 24.
More than 106,000 arrived from Ukraine in the last 24 hours, the highest figure since the war erupted.
The government in Romania - where nearly 200,000 Ukrainians have fled - was expected to approve a decree on Saturday to use a government buffer fund to finance the costs of housing an average of 70,000 people per day for 30 days.
But it wants EU help too.
Some 20,000 Ukrainians have entered Bulgaria, border police said.