The Security Council meeting on the Middle East had been brought forward from its original date of October 20, in order to discuss a UN report that accused Israel of war crimes and crimes against humanity.
The report, which was written by a panel led by Richard Goldstone, a South African judge, also accused Hamas, which has de facto control of Gaza, of violations, but reserved most of its criticism for Israel.
Al-Maliki told Al Jazeera that the PA's "intention is to shed light on the report and to prepare the stage for what will happen at the UN Human Rights Council [which sponsored the Goldstone report and which is set to re-open a debate on Thursday about the report, at the request of the PA]".
"I think it is very important when 44 countries participate in the deliberation, highlighting the important of the report," he said.
But Gabriela Shalev, Israel's ambassador to the Security Council, did not refer at all to the Goldstone report during the meeting on Wednesday, but dismissed its findings before the debate even began.
"I regret to say that the Goldstone report is one-sided, biased and therefore wrong - just as the forum and mandate that established its mission," she said.
Ban Ki-moon, the UN secretary-general, urged Israel and the Palestinians to hold domestic investigations into the allegations of war crimes.
Ban "calls upon 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 Security Council meeting.
"He hopes that such steps will be taken wherever there are credible allegations of human rights abuses throughout the world," he said.
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 within six months.
The report accused Israel of using disproportionate force during its war against Gaza-based Palestinian fighters.
It also accused the Israeli military of failing to protect civilians during its series of attacks on Gaza.
Israeli officials have condemned the 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.