Trickles of Ukrainians escape, but millions more are trapped in dire conditions

A tiny trickle of refugees have managed to flee Ukrainian cities under attack from Russian forces, but concerns are mounting for millions of people who remain trapped amid worsening conditions.

On Wednesday, Ukraine's Deputy Prime Minister Iryna Vereshchuk said both sides had agreed to a ceasefire and planned humanitarian corridors from a number of cities in order to allow people to leave.

The corridors will operate from 9 a.m. to 9 p.m local time, and routes include Energodar to Zaporizhia; Mariupol to Zaporizhia; Volnovakha to Pokrovsk; Izium to Lozova; and four separate routes from Vorzel, Bucha, Irpin, Borodyanka, and Gostomel to the capital city of Kyiv.

People huddle in a bomb shelter in Mariupol on Sunday.

A corridor will also operate between Sumy and Poltava, a route that enabled about 5,000 Ukrainians to evacuate on Tuesday, according to Ukrainian Presidential Office Deputy Kirill Timoshenko.

At least 2 million refugees have fled Ukraine since the beginning of the invasion, the UN estimates. But millions more remain trapped in towns and cities that have come under sustained attacks by Russian forces in recent days.

And on Tuesday Ukrainian Minister of Defense Oleksii Reznikov claimed more than 400 civilians have been killed, including 38 children, with the real death toll expected to be higher.

Reznikov accused Russia of "a real act of genocide" and "war crimes," claiming that Russian forces had even fired on humanitarian corridors.