Israel and its allies have repeatedly chastised the council for allowing majority-Muslim states to pass a steady stream of resolutions each session denouncing abuses against the Palestinians.
In her speech, the ambassador reiterated America's commitment to protecting human rights, closely linked to peace and security.
The Trump administration has also strongly criticized the United Nations for a Security Council resolution previous year that condemned Israeli settlement construction on the occupied Palestinian territories.
The council's critical stance of Israel has always been a contentious issue for the US, Israel's main ally.
While Haley has escalated those criticisms since becoming Washington's United Nations ambassador, her Tuesday speech was mild compared to past remarks, including an assault she levelled in a June 2 Washington Post op-ed.
John Fisher, Geneva director of the US-based Human Rights Watch, did not appear to fear an immediate withdrawal. It was the first such visit in 11 years.
At the council's annual June session, United Nations rights chief Zeid Ra'ad Al pointed the finger at members that are not cooperating with global experts who want to shed light on abuses.
"The world's foremost human rights body has tarnished the cause of human rights" by giving seats to brutal regimes, Haley charged.
Tobacco kills 7 million a year
In the event of the companies paying such taxes, he said, the revenue generated should be used to finance health delivery. Darko, mentioned the prohibition of smoking in public places, advertising prohibition and sponsorship as examples.
On Tuesday, she said the U.S.is "reviewing its participation" in the 47-member Council over its alleged "chronic anti-Israel bias". Former President George W. Bush boycotted the council over concerns that its membership included too many repressive governments.
The UN Human Rights Council works to address situations of issues against LGBT communities, as well as racial and ethnic minorities, women's rights and much more.
"We will always be leaders in the environment".
She added: "It is hard to accept that this council has never considered a resolution on Venezuela and yet it adopted five biased resolutions, in March, against a single country, Israel". "We seek to reestablish the council's legitimacy".
KELEMEN: Speaking via Skype, Donahoe, who's now at Stanford University, says after the USA joined the number of resolutions against Israel went down while the council had meetings on Syria and Libya. The letter followed public statements by Secretary of State Rex Tillerson that the United States will leave the Council if it does not reform.
The possible withdrawal represents another move away from multilateralism for the USA, after it stepped back from the Paris Climate Change Agreement last week.
Haley is scheduled to visit Israel later this week.
Ambassador Haley's comments are the closest the Trump administration has come to acknowledging human impact on climate change.
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