Abbas had angrily rejected a leading USA role in brokering peace talks after Trump's December 6 recognition of Jerusalem as Israel's capital, but in his United Nations speech he called for convening a peace conference in mid-2018 with "broad worldwide participation" but one in which the "foremost" conveners were the five permanent members of the Security Council and the members of the Quartet, the four entities guiding Middle Eastern peacemaking.
"It has become impossible today for one country or state alone to solve a regional or worldwide conflict", Abbas said.
As for Russia's proposal to hold a Palestinian-Israeli-Russian meeting, Maliki said Russia is still insisting on playing a positive role despite the obstacles, topped by Israel's rejection.
In December, the General Assembly voted 128-9, with 35 abstentions, to reject the United States decision to recognize Jerusalem.
The Palestinian leader immediately left the council chamber following his address, leaving Israeli ambassador Danny Danon to complain that he was once again "running away" from dialogue.
"You don't have to like that decision, you don't have to praise that decision", she said.
US President Donald Trump's son-in-law and senior adviser, Jared Kushner, and US Middle East envoy Jason Greenblatt sat behind Haley at the Security Council meeting.
"These enormous security and humanitarian challenges throughout the region should occupy more of our attention, rather than having us sit here month after month and use the most democratic country in the Middle East as a scapegoat for the region's problems", she said. Haley said the body should focus attention on other problems in the Middle East, such as the humanitarian crises in Yemen and Syria and the terrorist-sponsoring regime of Iran's role in the region's violence.
Abbas to address UN Security Council: “Israel is closing the doors on two-state solution”
The Israeli-Palestinian peace process has been deadlocked since a major push by the administration of Trump's predecessor Barack Obama ended in failure in April 2014.
Mr Trump has repeatedly said his administration is working up a new peace plan.
Israel, which often accuses both the European Union and the United Nations of bias against it, would be reluctant to accept any other mediator than the US.
France, which hosted a Middle East peace conference in Paris previous year, said it was ready to examine Abbas' proposal for a revamped approach.
Palestinian spokesman Nabil Abu Rudeina said Abbas would center his speech around "Al-Quds", or Jerusalem, and on basic Palestinian principles.
The plan also gears up for an worldwide conference to pave the ground for negotiations while committing to the two-state solution and the establishment of an independent Palestinian state with East Jerusalem as its capital, he said. Following the veto, a almost identical text was adopted at the General Assembly with 128 votes in favour, nine votes against, 35 abstentions and 21 absences.
Fourteen of the 15 security council members backed a similar resolution but it was vetoed by the US. "Is it for the two-state solution or the one-state solution?" he added.
Tensions have also flared over the U.S. decision to cut funding to the United Nations agency for Palestinian refugees (UNRWA).
Flights cancelled in New Zealand
Climate experts are predicting New Zealand will mark one of its hottest summers since records were first kept in the 1860s. Cyclone Gita hit the Pacific island nations of Fiji and Tonga last week, packing winds up to 275 km/h.
Manchester United to host Brighton in FA Cup quarter-finals
Southampton will join Brighton in Saturday night's draw for the last eight after seeing off West Bromwich Albion at the Hawthorns. Chris Hughton's side virtually sealed victory just after the hour-mark, as Leonardo Ulloa headed home from Bruno's cross.
Samsung shares hurt by negative Morgan Stanley forecast
The company will be starting construction soon on a special EUV facility as part of their Hwaseong complex in South Korea. The Note 8 has seen an incredible return to form for the company and saw over 4 million devices sold around the world.