Greenblatt and other USA officials have stated numerous times that they expect the Palestinians to recognize Israel as a Jewish state and rein in terror groups.
The official said the two sides discussed United States peace efforts as well the Palestinian reconciliation process.
The Times of Israel reports that Saudi King Salman Abdulaziz Al Saud and Crown Prince Mohammad bin Salman brought Abbas in for a meeting and told him to "accept Trump's peace plan or quit" as well as to rebuff any Iranian efforts to influence the PA.
"The truth is, that report is nonsense", he said.
The Saudi authorities, according to the report, made clear that they were dismayed by media images of Hamas's deputy political leader, Saleh al-Arouri, visiting Tehran in October.
Majdalani also said that Saudi Arabia's top leaders said their country is prepared to increase its economic assistance to the PA. Hamas has ruled Gaza since ousting the Fatah-dominated PA in 2007. Iran has said it will continue to back Hamas's military.
Last week, Lebanese prime minister Saad Hariri turned up in Riyadh, appearing on Saudi TV to announce his resignation and prompting rumors that he was being held against his will.
The planned deal comes after 10 months of studying the conflict from all perspectives, the report quoted White House officials as saying, and the plan will "address such perennial dividing points as the status of Jerusalem and settlements in the occupied West Bank".
The initiative calls on Israel to accept the establishment of a Palestinian state along 1967 borders and a "just solution to the Palestinian refugee problem" based on UN Security Council resolution 194, in exchange for the Arab world establishing normal relations with the Jewish state.