"The French president has expressed his concern at the possibility of the United States unilaterally designating Jerusalem as capital of the state of Israel," a statement said, referring to a phone call between the two leaders.
Any such decisions must be "within the framework of negotiations between Israelis and Palestinians, aimed in particular at the establishment of two states, Israel and Palestine, living side by side in peace and security with Jerusalem as capital," it added.
The Palestinian Islamist movement Hamas, which controls Gaza, called Saturday for a new "intifada" if Washington recognises Jerusalem as the capital of Israel or moves its embassy to the disputed city.
Officials say that move is unlikely to be taken outright, but Trump may instead deliver a speech later this week recognising Jerusalem as Israel's capital.
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The status of Jerusalem is a key issue in the Israeli- Palestinian conflict.
Both Israelis and Palestinians claim the city as their capital and previous peace plans have stumbled over debates on whether, and how, to divide sovereignty or oversee holy sites.
The Palestinian president's office told AFP on Friday that American recognition of Jerusalem as the capital of Israel would "destroy the peace process".
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