Ukraine's President Volodymyr Zelenskyy said around 100,000 people more people were evacuated from the country in two days.
He also reportedly took a dig at Russia for targeting a humanitarian corridor in the city of Mariupol.
Zelensky said he decided to send a convoy of trucks into the besieged port city with food, water and medicine. But "the occupiers launched a tank attack exactly where this corridor was supposed to be", he said in a video statement, describing it as "outright terror".
The Ukrainian leader said that, of the around 100,000 people who had been able to leave other Ukrainian cities via humanitarian corridors over the past two days, some 40,000 had fled yesterday alone.
Ukraine has accused Russia of carrying out an airstrike on Wednesday on a maternity hospital in Mariupol, a strategic port on the Azov Sea, killing three people, including a young girl.
Moscow yesterday promised to open humanitarian corridors every day to allow Ukrainians to flee onto its soil, but Kyiv has previously rejected evacuation routes leading into Russia.