Petro Andryushchenko said the situation in the Ukrainian city was “catastrophic” and warned the death toll would approach 350,000 if residents did not leave in time.
He told the Present Time TV channel: “Four days ago, we talked about an ‘optimistic’ scenario - about 10,000 victims today. But with the increased intensity and the brutality that has increased many times over, we can say that if the blockade ends now and we can start at least searching for these people, the number of victims is already approaching 20,000.
“But if this does not happen in the coming days, this number will approach 350 thousand - all those who did not have time to leave.”
Meanwhile, Ukraine will make a new attempt to deliver supplies to civilians trapped in the encircled city of Mariupol on Tuesday, Deputy Prime Minister Iryna Vereshchuk said.
She made her announcement as Vitaliy Koval, the governor of the northern region of Rivne, said the death toll from a Russian air strike on a television tower in his region on Monday had risen to at least 19.
Moscow on Monday allowed the first convoy of civilians to escape Mariupol, but a senior presidential aide said Russia had again blocked a humanitarian aid convoy trying to reach the city with supplies.
Obtaining safe passage for aid to reach Mariupol and for civilians to leave has been Kyiv's main demand at several rounds of talks. Previous attempts at a local ceasefire in the area have failed. Read full story
Vereshchuk said a convoy with humanitarian supplies would head for Mariupol on Tuesday.
"On the way back it will pick up women and children," she said.
Civilians have been trapped in the southern port city by Russian shelling for more than two weeks and have been without heating, electricity and running water for most of this time, the Ukrainian authorities say.
China has today denies claims by US officials that Russia sought military assistance in Ukraine and accused Washington of spreading "malicious disinformation" that risked escalating the conflict.
"The US has repeatedly spread malicious disinformation against China on the Ukraine issue," the Chinese embassy in London told Reuters in a statement.
"China has been playing a constructive role in promoting peace talks," it added.
"The top priority now is to ease the situation, instead of adding fuel to the fire, and work for diplomatic settlement rather than further escalate the situation."
Several US officials said Russia had asked China for military equipment after its February 24 invasion of Ukraine, sparking concern in the White House that Beijing might undermine Western efforts to help Ukrainian forces defend their country.
A series of Russian strikes hit a residential neighborhood of Ukraine’s capital on Tuesday, igniting a huge fire and frantic rescue effort in a 15-storey Kyiv apartment building.
At least one person was killed and others remain trapped inside.
The Ukrainian military said in a statement that the strikes were artillery strikes.
They hit the Svyatoshynskyi district of western Kyiv, adjacent to the suburb of Irpin that has seen some of the worst battles of the war.
Flames shot out of the apartment building as firefighters rescued people from ladders. Smoke choked the air.
A firefighter at the scene confirmed one person died and that several have been rescued alive but others are still inside as rescuers try to reach them.