The Palestinian Hamas movement has called for a new "intifada" if Washington recognises Jerusalem as the capital of Israel or moves its embassy to the disputed city.
Officials in Washington say Trump is considering recognising Jerusalem as Israel's capital as a way to offset his likely decision to delay his campaign promise of moving the US embassy there.
Israel regards Jerusalem as its capital, a position nearly the entire world rejects saying its status should be determined in peace talks with the Palestinians.
East Jerusalem is considered occupied Palestinian territory under international law and its future status is a key issue in the Israeli-Palestinian conflict.
"We warn against such a move and call on the Palestinian people to revive the intifada if these unjust decisions on Jerusalem are adopted," Hamas said in a statement.
Any decision to move its embassy there would be "a flagrant attack on the city by the American administration" and give Israel "a cover for continuing its crime of Judaising the city and emptying it of Palestinians", it said.
The Second Intifada - which claimed the lives of some 3,000 Palestinians and 1,000 Israelis - was sparked by the visit of right-wing opposition leader Ariel Sharon to Jerusalem's flashpoint al-Aqsa Mosque compound in 2000.
On Friday, the office of Palestinian President Mahmoud Abbas said that US recognition of Jerusalem as the capital of Israel would "destroy the peace process".
Since 1995, it has been US law that Washington's embassy in Israel must be moved from Tel Aviv to Jerusalem, as demanded by Israel.
But every six months since the law was passed a succession of US presidents have signed a waiver to hold off on a move which would enrage Palestinians, the international community and the Arab world.
Trump has signed the waiver once, and grudgingly, after vowing to Jewish-American supporters that he would be the president to finally make the switch permanent.
The next deadline comes on Monday, and some in Washington suggest that Trump is planning a speech on the issue next week, before his deputy Mike Pence heads to Jerusalem.
The White House has described reports he may refuse to sign the waiver as premature - but sources told AFP they expect Trump to formally declare Jerusalem Israel's capital.