American officials have said Mr Trump may recognize Jerusalem as Israel's capital this week as a way to offset his likely decision to delay his campaign promise of moving the US embassy there.
His point-man on the Middle East, son-in-law Jared Kushner, later said the US President hasn't decided yet what steps to take regarding Jerusalem.
The diplomatic adviser of President Mahmoud Abbas said the Palestinian leadership would "stop contacts" with the United States if Mr Trump recognised Jerusalem and Israel's capital.
Majdi Khaldi said the US would lose credibility as a mediator in the Middle East if the US President went ahead with the move.
Israel captured east Jerusalem, which is home to major Muslim, Christian and Jewish holy sites, in the 1967 Middle East war.
It quickly annexed it, declaring the whole of the city as its capital in a move which has not been recognised internationally.
Palestinians want Jerusalem as the capital of their future state and the international community argues the city's status must be determined in peace talks.
The possibility of Mr Trump recognising Jerusalem as Israel's capital has also stirred opposition from US and foreign officials, who fear it could unleash violence.
Such a decision, which US officials have said has not been finalised, would violate decades of US policy not to take a stance on the fate of Jerusalem, on the grounds it was an issue Israeli sand Palestinians should negotiate and decide.
It could spark demonstrations or violence by Palestinians or Muslims around the world, in part because of the sensitivity of the Jerusalem site known to Jews as the Temple Mount and to Muslims as Haram al-Sharif.
The site includes the al Aqsa Mosque, the third-holiest site in Islam, and the golden Dome of the Rock. It was also the site of an ancient Jewish temple, the holiest place in Judaism.
On Monday, the White House said it would not take any action on whether to move the US embassy from Tel Aviv to Jerusalem, something Mr Trump promised to do in his presidential campaign.