As reported by Censor.NET citing Reuters, Hungary received 144 votes, followed by Croatia with 114 votes and Russia with 112 votes.
The Guardian reports that General assembly failed to vote for Russia to be one of 14 new members after campaign by rights groups over its bombing of Syria.
Russia has lost its bid to become a member of the UN's human rights council, in a defeat that reflects the diplomatic cost of its war in Syria.
Russia was beaten on Friday by Hungary and Croatia in the competition for two seats on the council allotted to eastern European states.
It was the first time one of the permanent five members of the security council had failed to get elected to the HRC since its formation a decade ago, and followed a campaign by human rights groups opposing Russian membership because of its role in the bombing of Syrian cities, eastern Aleppo in particular.
"They bomb a hospital one day, they run for the Human Rights Council the next. And they wonder why they missed the cut," a western diplomat said.
Vitaly Churkin, the Russian envoy, shrugged off the rebuff, saying the countries who beat Russia "are not as exposed to the winds of international diplomacy."
"Russia is quite exposed," Churkin said.
Human rights groups also campaigned against Saudi Arabia for the high civilian death toll of its bombing campaign in Yemen, but the kingdom won one of the four seats reserved for the Asia-Pacific region.
The 193-member general assembly on Friday elected 14 members to the 47-nation council, the UN's main body charged with promoting and protecting human rights.
Brazil, China, Cuba, Egypt, Iraq, Japan, Rwanda, South Africa, Tunisia, the UK and the US were also elected to the council.
At the same time as Russia suffered its diplomatic setback, the Kremlin announced that president Vladimir Putin had turned down the Russian military's demand to resume bombing of Aleppo, to keep open humanitarian corridors for rebels and civilians to leave the city.
"In rejecting Russia's bid for re-election to the Human Rights Council, UN member states have sent a strong message to the Kremlin about its support for a regime that has perpetrated so much atrocity in Syria. It also shows how important it is to have competitive slates in UN elections," Louis Charbonneau, UN director at Human Rights Watch, said.
"Countries should have a chance to reject those whose candidacies are so severely compromised, as they did today. We have already said that Saudi Arabia, which was re-elected without competition, doesn't belong on the council in light of its indiscriminate attacks on civilians in Yemen. We'll be keeping all members' rights records under the microscope while they're on the council. Next year, UN member states should make sure that all regional groups have real competition so no one is guaranteed victory," he said.
Russia currently holds the presidency of the UN security council but has alienated many UN member states by its support for the Syrian regime's airstrikes against rebel-held cities, and by its verbal attacks on UN officials who had criticised the airstrikes. On Thursday, Churkin shrugged off the findings of a UN investigation that the Syrian regime had used chemical weapons, saying the regime itself should have its own enquiry.
"Russia deserves this defeat, but it will only increase Moscow's contempt for the UN," said Richard Gowan, a UN expert at the European Council for Foreign Relations. "The Russians only really care about the security council anyway, and they may well respond by stirring up more trouble there over Syria or other crises."
In 2001, the US was voted off the HRC's predecessor, the UN Human Rights Commission, in a gesture of disapproval over the George Bush administration's unilateralist leanings.