He added that local authorities and police were starting to stabilise the city and the region.
Jubilant residents welcomed Ukrainian troops arriving in the centre of Kherson on Friday after Russia abandoned the only regional capital it had captured since the start of the war.
"Before fleeing from Kherson, the occupiers destroyed all the critical infrastructure: communications, water, heat, electricity," Zelensky said in his daily video address on Saturday adding that almost 2,000 mines, trip-wires and unexploded shells had been dealt with so far in the area.
Authorities have been able to bring back local TV and radio transmissions on a platform provided by a Polish company, Poland’s PAP news agency said on Saturday.
"[Russians] everywhere have the same goal: to humiliate people as much as possible. But we will restore everything, believe me," Zelensky went on to say in his video.
He said Ukrainian troops had taken control of more than 60 settlements in the Kherson region.
“In the towns and villages that are still under occupation, we are not forgetting anyone and we will not leave anyone behind,” Zelensky stressed.
“Through our defensive operations and diplomacy, we will finally have our national borders recognised internationally,” he added.
But pro-Moscow forces are putting up a much stiffer fight elsewhere and Zelensky said the battles in the eastern Donetsk region were hellish.
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Sources: IAR, Reuters