The rights group had warned that the proposed changes could trigger "hostile amendments", possibly from China and Russian Federation, to undermine the work of the council which monitors human rights crises worldwide.
The European Union said the move "risks undermining the role of the USA as a champion and supporter of democracy on the world stage", while British Foreign Secretary Boris Johnson called it "regrettable". For example, she notes that resolutions focused on Israel's human rights record have fallen from around 40 percent of the council's annual totals in 2009 to about 20 percent a year ago.
The US withdrawal "only serves to empower actors on the council, like Russian Federation and China, that do not share American values on the preeminence of universal human rights", Freedom House and 11 other worldwide rights organizations said in a letter to Haley and Secretary Pompeo.
The US and Australia cast the only no votes at the time, while the Israeli ambassador in Geneva attacked the council for "spreading lies against Israel".
Haley criticized the non-governmental organizations in a letter the day after she announced the US was exiting the council.
But Haley cited longstanding USA complaints that the 47-member council is biased against Israel.
"This is not about a hard-power security umbrella, but a moral security umbrella that so many around the world have come to count on over the last seven decades that the United States has played this role of champion of human rights", says Melissa Labonte, an associate professor and expert in multilateral peace operations and human rights promotion at Fordham University in NY.
And the Heritage Foundation, a conservative think tank close to the Trump administration, defended the move, calling the council "notably incurious about the human rights situations in some of the world's most oppressive countries".
"You know, we're actually self-governing in this country".
Human Rights Watch UN director Louis Charbonneau said it is "preposterous" to suggest rights groups were undermining reform attempts, and called claims of them backing Russian Federation and China "absurd".
But human rights groups voiced fresh complaints about the body in 2013, after China, Russia, Saudia Arabia, Algeria and Vietnam were elected members.
"In the larger scheme of things, this really is a way of standing by its ally, Israel, but also using the opportunity to try to exert its own vision of human rights - even though a number of global human rights groups are roundly criticising the Trump administration for leaving the council".
Since January 2017, it has announced its withdrawal from the Paris climate accord, left the United Nations educational and cultural organization and pulled out of the Iran nuclear deal.
Washington's withdrawal is the latest USA rejection of multilateral engagement after it pulled out of the Paris climate agreement and the 2015 Iran nuclear deal.
The US' move is unprecedented in the 12-year history of the council, as no country has ever dropped out voluntarily.
Beyond the case of Israel, these same critics have called on the Geneva-based council to address its other glaring shortcomings. Libya was kicked out seven years ago.
Under President Barack Obama, who was sworn in as president in 2009, the U.S. was elected to the body for the maximum two consecutive terms.
Bolton - who has long opposed the council -voted against creating it, while he was serving as ambassador to the United Nations back in 2006. After a year off, it was re-elected in 2016.