Refugees arrived on buses from Mariupol in the south east Ukrainian city of Zaporizhzhia after finding transport chartered by volunteers.
Some drove their personal cars, decorated with a white ribbon to show they are civilians.
"We walked for almost 15 kilometres with a 6 year-old child and a teenager," said Tatiana, a doctor who lived in Mariupol. "We walked despite the mines, the Grad and the rockets."
She said the city barely exists anymore with some 90 per cent of houses there destroyed.
Further north, in the city of Lysychansk, almost half of the 100,000 people who live in the city have already left.
Lysychansk has become a transit town for those who are fleeing from places far worse.
Ukrainian officials announced on Saturday that there were seven humanitarian corridors to evacuate people in the east of the country, where heavy fighting has taken place.
Millions of Ukrainians have been internally displaced since the beginning of the war on 24 February and more than 4.1 million have fled the country, according to the United Nations' Refugee Agency.
Around 120 people arrived at the airport in Moldova on Friday as part of the second humanitarian flight initiated by the German government.
Nearly 400,000 Ukrainians have fled to the neighbouring country since the beginning of the war.