The UN Refugee Agency chief Filippo Grandi said the numbers of people on the move was "extremely worrying" "We are looking at what could become Europe"s largest refugee crisis this century," he said GENEVA: Some 677,000 refugees have fled the conflict in Ukraine for safety in neighbouring countries, while around a million people are estimated to be internally displaced, the United Nations said Tuesday. The UN Refugee Agency chief Filippo Grandi said the numbers of people on the move was "extremely worrying", as Russian troops pound cities in eastern Ukraine, on day six of Moscow"s invasion. Grandi told a press conference in Geneva that the latest figure he had was 677,000 people who had fled from Ukraine to neighbouring countries. "We are looking at what could become Europe"s largest refugee crisis this century," he said. Grandi said that around half had fled to Poland, whilst roughly 90,000 had reached Hungary, 60,000 Moldova, 50,000 Slovakia and 40,000 Romania. At an earlier press conference, Shabia Mantoo, a spokeswoman for UNHCR, the UN Refugee Agency, said the numbers were "exponentially increasing". She said that all neighbouring countries had so far kept their borders open for refugees fleeing Ukraine -- including a "sizeable number" who have crossed into Russia. "UNHCR urges governments to continue to maintain access to territory for all those fleeing: Ukrainians, and third-country nationals living in Ukraine, who are now forced to escape the violence," she said. Meanwhile in Stockholm, Karolina Lindholm Billing, the UNHCR representative to Ukraine, estimated that a million people had been internally displaced by the Russian invasion. "We estimate that it has to be about one million people who have fled internally or who are currently on a train, a bus or in a car trying to get to a safety," she told a press conference in Stockholm. She cautioned that the agency still did not have reliable figures. Mantoo said that at the Polish border, UNCHR staff reported that people who managed to cross the frontier had been waiting up to 60 hours in freezing temperatures. "Refugees who have the means are finding their own accommodation, whereas others are being hosted with local communities who have opened their homes, or sheltered in reception centres," she said. There are queues of up to 20 hours to enter Romania, said Mantoo, with volunteers providing interpretation services, while it is taking 24 hours to cover the 60 kilometres (37 miles) between the Ukrainian port city of Odessa and the border with Moldova. New arrivals in Moldova are being accommodated in temporary reception centres, while the UNHCR is distributing relief items, including blankets and sleeping bags, with an airlift from Dubai of more supplies due to arrive on Wednesday. The UN"s International Organization for Migration said an estimated 470,000 third-country nationals were living in Ukraine, including a large number of overseas students and labour migrants. "While 6,000 of those have been confirmed to have arrived in Moldova and Slovakia alone, many remain stranded amidst the worsening security situation," spokeswoman Safa Msehli told journalists in Geneva. "We appeal to states to protect people forced from their homes due to the fighting and to allow them to cross Ukraine"s borders to safety -- without discrimination."