Ukraine accused Russia of blowing up the dam, which crosses the Dnipro river, flooding the surrounding area with landmine-contaminated water and leaving areas upstream without water supply.
Moscow has denied responsibility.
"The stark figures speak for themselves. The destruction of the Kakhovka dam has resulted in a staggering loss and damage," said Christophoros Politis, the United Nation Development Programme's deputy resident representative in Ukraine, at a presentation in Kyiv.
The preliminary figures put the damage and losses at $13.79 billion, taking into account the environmental toll, the loss of power generation, irrigation for farming and housing as well as other factors.
The destruction of the dam "is foreseen to have severe, enduring consequences on Ukraine's environment, economy and society", a post-disaster needs assessment report said.
The report identified the lasting environmental impact as its biggest concern.
"The figures are massive... and add to the economic burden on Ukraine," Politis said.
A joint report by the World Bank, United Nations, European Commission and the Ukrainian government previously estimated the cost of reconstruction and recovery at $411 billion from damage caused during the first year of the war.
"All sectors have been heavily impacted, from health care, water supply facilities to energy and community infrastructure to housing and livelihoods," Politis said.
The UN added that it does not know the extent of damage to Russian-occupied areas of the Kherson region, where the dam was located.
Ukraine's state-owned hydroelectric company Ukrhydroenergo said that it is also not possible to examine the damage to the dam itself.
"No access is available because it is very close to the hostilities," said a company representative, Oleg Ososkov.
Despite the ongoing war, officials said that recovery efforts continue.
"You need to provide water right now for people and there is support going on for that, there is infrastructure building for that," said Ukrainian deputy economy minister Oleksiy Sobolev.
"It is important to highlight and to stress that recovery will take years but it has started today," Politis said.
The UN says it supports rebuilding the dam or installing other renewable energy systems as part of medium-term plans for a green recovery in Ukraine.
"The opportunity is unique... for Ukraine to rethink the future of all that area in a greener, modern, sustainable and climate-friendly way," said Politis.
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