Mr Zelensky also called for allies to provide “effective counteraction” against Moscow’s advances after holding talks with Boris Johnson on Friday morning.
Downing Street said the Prime Minister pledged further support “in the coming days” after the president updated him on the “terrible developments” in the Ukrainian capital.
Defence Secretary Ben Wallace said more than 450 Russian troops had been killed, as a fierce resistance meant Moscow “failed” on the main objective on the first day of fighting.
Mr Johnson and Mr Zelensky spoke after Kyiv was hit by “horrific rocket strikes” and fighting reached the outskirts of the capital overnight.
After the call, the president said Ukraine “needs the support of partners more than ever”.
“We demand effective counteraction to the Russian Federation. Sanctions must be further strengthened,” Mr Zelensky added.
Mr Johnson unveiled the “largest and most severe” package of sanctions Russia has faced to punish Vladimir Putin, hitting further oligarchs and freezing Russian bank assets.
The Kremlin retaliated to the ban on Aeroflot planes touching down in Britain by banning UK flights to and over Russia on Friday.
Mr Johnson assured Mr Zelensky that “the world is united in its horror at what Putin is doing” and praised the “bravery and heroism of the Ukrainian…