A Jordanian palace statement quoted King Abdullah as telling the US president that such a decision would have "dangerous repercussions on the stability and security in the region" and would obstruct US efforts to resume Arab-Israeli peace talks.
"Jerusalem is the key to achieving peace and stability in the region and the world," the statement added.
Palestinian President Mahmoud Abbas also joined a mounting chorus of warnings.
Abbas "warned of the dangerous consequences such a decision would have to the peace process and to the peace, security and stability of the region and of the world," his spokesman Nabil Abu Rdainah said.
The status of Jerusalem is a critical issue in the Israeli-Palestinian conflict, with both sides claiming the city as their capital.Palestinians called for three days of protests starting from Wednesday, raising fears of potential unrest.
Israel seized the largely Arab eastern sector of Jerusalem during the 1967 Six-Day War and later annexed it, claiming both sides of the city as its capital.
But the Palestinians want the eastern sector as the capital of their future state and fiercely oppose any Israeli attempt to extend sovereignty there.
Trump was pushed to act on the embassy as a result of the 1995 Jerusalem Embassy Act, which stated that the city "should be recognised as the capital of the state of Israel" and that the US embassy should be moved there.
A waiver has been repeatedly invoked by successive US presidents, postponing the move on grounds of "national security" once every six months, meaning the law has never taken effect.