Amnesty International and Human Rights Watch said they would begin lobbying the UN General Assembly to hold a vote on suspending Saudi Arabia from the Geneva-based council, even though they admitted this was a long shot.
"Over the past few months, Saudi Arabia has gone beyond the pale and does not deserve anymore to sit on the Human Rights Council," said HRW deputy director Philippe Bolopion.
Human Rights Watch accused Riyadh of targeting civilians in the war in Yemen, using cluster bombs banned by international conventions and laying siege to ports to prevent basic goods from reaching Yemen.
The joint appeal again put the spotlight on Saudi Arabia, which has been leading an Arab coalition carrying out air strikes against Huthi rebels and their allies who seized much of Yemen.
The coalition is supporting Yemen's President Abedrabbo Mansour Hadi in a war that the UN says has killed more than 6,400 people, about half of them civilians since March 2015.
"Saudi Arabia is in a league of its own," Bolopion told a news conference, adding that the kingdom is "getting away with murder in a way that no other country has been able to do."
The rights groups charged that Saudi Arabia had used its position as a council member to block an independent international investigation of war crimes in Yemen.
Riyadh pressured UN Secretary-General Ban Ki-moon to remove the coalition from a blacklist of child rights violators by threatening to withdraw funding to UN aid programs.
Saudi Arabia has denied using pressure tactics and insists the coalition is not deliberately targeting civilians in Yemen.
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Saudi Foreign Minister Adel al-Jubeir dismissed the accusations as "outrageous."
"The coalition is very cautious in selecting targets. We do not harm civilians," the minister told reporters in Paris.
Repression at home
Amnesty International said the Saudi government had brutally cracked down on dissent at home and resorts to executions for offenses that under international law are not punishable by the death penalty.
Since 2013, all prominent human rights defenders in Saudi Arabia have been either thrown into prison, threatened into silence or have fled the country, said Richard Bennett, Amnesty's UN director.
Saudi Arabia was elected by the assembly in 2013 to sit on the 47-member council and a two-thirds majority would be needed to remove it from the body, which the rights groups and UN diplomats admitted would be unlikely.
Libya is the only country ever to suspended from the council by a vote held in 2011 to protest Moamer Kadhafi's violent crackdown on protesters.
The rights groups said Saudi Arabia had managed to get away with such violations because of support from the United States and Britain.
HRW's director for the Middle East, Sarah Leah Whitson, said the United States and Britain had "crossed the threshold to be part of this war" in Yemen by supplying weapons and supporting operations.
The rights group is asking the Pentagon to provide information on how it is supporting the coalition with the choice of targets, said Whitson.
This form of military assistance would make the United States complicit in war crimes, she said.