The Geneva debate comes a day after the UN Security Council discussed the report, during which the Palestinian Authority demanded that Israel be punished for war crimes.
In the report released last month, investigators led by South African jurist Richard Goldstone accused both Israel and the Palestinian group Hamas of war crimes in Gaza, but were overall more critical of Israel than Hamas.
The Palestinian Authority had initially agreed to defer a vote on the UN-sanctioned report but later backtracked under heavy criticism.
The Palestinians in a draft resolution circulated for the human rights council debate, called on Ban Ki-moon, the UN secretary general, to monitor whether Israel and Hamas conduct credible investigations.
The council is expected to vote on adopting the resolution on Friday.
It "strongly condemns all policies and measures taken by Israel, the occupying power, including those limiting access of Palestinians to their properties and holy sites" and calls on Israel to stop digging and excavation work around the Al-Aqsa mosque as well as other Islamic and Christian religious sites.
In her speech, Pillay cited concern about the restrictions on Palestinians wishing to enter Al-Aqsa and expressed "dismay" about the Israeli blockade of Gaza that she said "severely undermines the rights and welfare of the population there".
Israel rejected the charges saying the resolution – drafted by the Palestinians with Egypt, Nigeria, Pakistan and Tunisia, on behalf of non-aligned, African, Islamic and Arab nations – threatened peace efforts.
Binyamin Netanyahu, the Israeli prime minister, said on Thursday that his country would not be able to take "risks for peace" if it could not defend itself from attacks on its citizens.
"It's important for the principle countries, outside of this automatic majority of the United Nations, to say we are not taking part in this.
"We know we should act otherwise," he said.
'Reward for terror'
Aharon Leshno Yaar, Israel's ambassador to the United Nations, said the adoption by the council of the proposed resolution would be a "reward for terror and will send a clear message to terrorists everywhere".
|Navi Pillay, right, has called for "independent and prompt" investigations [Reuters]
"They will clearly hear that this new form of warfare, as used by Hamas in Gaza, will offer immunity as countries will be prevented from waging effective responses.
"This strategy will be repeated in other places, against other countries fighting terror."
The Goldstone report recommended that its conclusions be sent on to the International Criminal Court (ICC) prosecutor in The Hague if Israel and Hamas do not hold their own credible investigations into allegations of war crimes within six months.
The report accused Israel of war crimes and crimes against humanity.
It also accused Hamas, which has de facto control of Gaza, of war crime violations, but reserved most of its criticism for Israel.
On Wednesday, Ban urged "all of the parties to carry out credible domestic investigations into the conduct of the conflict without delay", Lynn Pascoe, the UN under secretary general for political affairs, told the UN Security Council.
Israeli officials have condemned the Goldstone report, saying their country had a right to defend itself from Hamas rocket attacks.
But Desmond Travers, a retired army colonel who worked with Goldstone on the report, dismissed that response.
"We examined that very carefully ... but we ruled that this was not a justifiable argument," Travers, currently with the Institute for International Criminal Investigations, told Al Jazeera.
"This report has taken the world community at large one lurch forward into the whole question of impunity," he said.
"We cannot lurch back, and I think the world at large doesn't wish to do that."
About 1,400 Palestinians – the majority of them civilians - and 13 Israelis were killed during Israel's three-week war on Gaza between last December and January, which had the stated aim of stopping rocket attacks by Palestinian fighters from the coastal territory.