"I may. I may," Trump said in response to questions by a reporter during brief remarks at the White House alongside Israeli Prime Minister Benjamin Netanyahu. "If I can, I will."
The U.S. accelerated the planned move of its diplomatic headquarters from Tel Aviv to Jerusalem last month, hoping to hold the ceremonial opening on the same day Israel celebrates its 70th anniversary May 14.
The relocation was originally planned to be completed by the end of 2019.
The plan was the United States’ first priority after Trump announced in December his decision to recognize Jerusalem as Israel's capital, which drew a storm of condemnation from the international community, including Washington's close allies.
So far, no other country has followed Washington's lead, despite calls from Israeli leaders to do so, and the decision has upended American efforts to negotiate a Palestinian-Israeli peace deal that has been made even more elusive after the declaration.
Jerusalem's status was long considered a matter to be resolved in final status negotiations but Trump continued to insist Monday his decision has taken the decision off the table. Palestinians are seeking the east of the contested city as the capital of their state.
East Jerusalem has been occupied by Israel since 1967 and the Palestinian leadership has outright rejected a mediating role for the U.S. after the move to recognize Jerusalem as Israel's capital.
Trump said the Palestinians want to return to the bargaining table "very badly", adding "we have a shot" at brokering a peace deal.
Netanyahu thanked Trump for taking action on Jerusalem. "This will be remembered by our people through the ages. Others talked about it. You did it,” he said.
He also warned Iran is the U.S.'s and Israel's greatest security challenge.
"Iran has not given up its nuclear ambitions. It came out of this nuclear deal emboldened, enriched. It is practicing aggression everywhere, including on our own borders," Netanyahu said. "Iran must be stopped. That is our common challenge."