Nikki Haley, the US ambassador to the United Nations, also called for the council to adopt strong resolutions on abuses in Syria, Eritrea, Belarus, Ukraine and the Democratic Republic of Congo.
The Trump administration gave formal notice on Tuesday that it is reviewing its participation in the UN Human Rights Council and called for reforming the body to eliminate what it called its "chronic anti-Israel bias."
The body has taken a strong position against Israel's occupation of territory seized in the 1967 Middle East war, its treatment of Palestinians, and its building of Jewish settlements.
Most countries consider the settlements, in areas the Palestinians envisage as part of an eventual independent state, illegal.
The Council's critical stance of Israel has long been a contentious issue for the United States, Israel's main ally.
Washington says the Council is stacked with opponents of Israel and boycotted it for three years under President George W. Bush before rejoining under Barack Obama in 2009.
"The United States is looking carefully at this Council and our participation in it. We see some areas for significant strengthening," Nikki Haley, US ambassador to the United Nations, told the Geneva forum.
"Tragically, we've been down this road before," Haley later told the Graduate Institute of Geneva. "America does not seek to leave the Human Rights Council. We seek to reestablish the Council's legitimacy."
She named Venezuela, Cuba, China, Burundi, and Saudi Arabia as not upholding the highest standards despite their membership and said that the forum was becoming "discredited" like its predecessor body, the Human Rights Commission.
The 47-member Council adopted five "biased" resolutions on Israel and the Palestinian territory at its March session, but never even considered a resolution on Venezuela, she said.
"This relentless, pathological campaign against a country that actually has a strong human rights record makes a mockery not of Israel, but of the Council itself," Haley said, as some in the audience interrupted briefly with laughter at the remark.
She called for the Council to address serious human rights violations in Venezuela and for the government of President Nicolas Maduro to address them.
"If Venezuela cannot, it should voluntarily step down from its seat on the Human Rights Council until it can get its own house in order. Being a member of this council is a privilege, and no country who is a human rights violator should be allowed a seat at the table," she said.