In a Facebook post, Zelensky said: "This morning was not good, but it brought the truth. Even before the end of the International Commission, Iran had pleaded guilty to crashing the Ukrainian plane. But we insist on full admission of guilt.
"We expect from Iran assurances of a willingness to fully and openly investigate, bring those responsible to justice, return the bodies of the dead, pay compensation, and make official apologies through diplomatic channels," Xinhua news agency reported.
Zelensky said he hoped the investigation would continue without obstruction, adding that the actions of the personnel responsible for the downing should be investigated.
Earlier on Saturday, Iran admitted that its armed forces had downed the Kiev-bound Ukraine International Airlines (UIA) flight PS75 near Tehran killing all 176 people on board, adding that it was an "involuntary human error" and those responsible would "immediately" be held accountable.
Iran's Islamic Revolutionary Guard Corps (IRGC) said that the mistake was made in the context of a "very delicate crisis situation", claiming that the US-made Boeing 737-800 had flown close to a sensitive IRGC military centre with the "altitude and flight position of an enemy target".
The victims comprised 82 Iran, 63 Canad, 11 Ukrain, 10 Swedes, four Afghans, four Britons and three Germans.
Wednesday's crash occurred on the same day after Iran launched more than a dozen ballistic missiles at two US military bases in Iraq, in retaliation for the killing of Iranian Major General Qasem Soleimani in an American drone attack in Baghdad on January 3.
( With inputs from IANS )