Talks between Russian and Ukrainian representatives have become “more constructive”, although Mr Zelenskyy’s senior adviser described the discussions as a “difficult and viscous process”.
Around 20,000 people have fled Mariupol in what is believed to be the biggest evacuation yet from the besieged port city.
Around 570 of some 4,000 vehicles that left the city have reached Zaporizhzhia which is 160 miles (260km) northwest while others will spend the night in various towns along the way.
And while talks between Russian and Ukrainian representatives have become “more constructive”, the bombardment of Kyiv has been stepped up, with attacks on apartments and a subway station.
President Volodymyr Zelenskyy’s senior adviser described the talks as a “very difficult and viscous negotiation process”.
“There are fundamental contradictions. But there is certainly room for compromise. During the break, work in subgroups will be continued,” he added.
With the number of people driven from the country by the war eclipsing three million, large explosions thundered across the capital before dawn from what Ukrainian authorities said were artillery strikes.
Mayor Vitali Klitschko has brought in a curfew until 7am on Thursday (5am GMT).
People will only be able to move around the city with “special permission” except to “go to bomb shelters”, the mayor said.