"We have talked and carried out consultations with King Salman and Crown Prince Mohammed bin Salman since US President Donald Trump announced Jerusalem as the capital of Israel, also coordinated and discussed with them - along with the Arab brothers, the upcoming steps that should be taken", Abbas said, in his interview with Arrajol Magazine.
Abbas called President Donald Trump's decision earlier this year to move the US embassy in Israel to Jerusalem a "dangerous" development.
Haley was accompanied to the council meeting by Jason Greenblatt, the USA envoy for Middle East peace and Jared Kushner, Trump's son-in-law and adviser on Israeli-Palestinian peace efforts.
"But we will not chase after you", Haley said.
"We call for the convening of an global peace conference by mid-2018 based on worldwide law and the relevant United Nations resolutions", he said.
"We have expressed our absolute readiness to reach a historic peace agreement", Abbas said.
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.
"Ambassador Friedman made clear in his remarks that the President is committed to a comprehensive peace agreement that benefits both Israelis and Palestinians", the USA spokesperson explained, and assured that "the U.S.is working on a plan to achieve that goal".
The Middle East peace process has been gradually returning to the world's agenda, Al-Monitor reported.
He called for a "multi-level global coalition" that would replace America as the primary broker of the Israeli-Palestinian peace process.
In December, the General Assembly voted 128 to 9, with 35 abstentions, to reject Washington's decision to recognise Jerusalem.
Haley reiterated that "the United States stands ready to work with the Palestinian leadership".
"Israel has imposed colonial facts instead of Oslo to consolidate its control and sovereignty over the land, resources and the Palestinian people in order to implement the project 'Greater Israel in the historic land of Palestine, ' Abbas explained".