The housing would be the first approved in east Jerusalem since Trump called on Israeli Prime Minister Benjamin Netanyahu to curb settlement construction in February.
Trump's son-in-law and adviser Jared Kushner arrived in Israel last month and sat down with Israeli and Palestinian leaders in an effort to help kick-start long-dormant negotiations.
Kushner discussed potential actions to make progress toward "a genuine and lasting peace" between Israelis and Palestinians during his meeting with Netanyahu. But amid deep disagreements between the sides, he has not yet said how he plans to proceed.
"As we have demonstrated in recent trips and conversations with the parties, the Trump Administration is committed to and focused on doing everything possible to advance the prospects of a historic, conflict-ending agreement between Israelis and Palestinians," the statement added.
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City Hall said it will approve the 800 units in an upcoming planning committee meeting, along with 114 units in Arab neighborhoods.
Israel captured east Jerusalem during the 1967 Mideast war and annexed it, but the international community doesn't recognize Israeli sovereignty. Palestinians hope to establish their capital of a future state in east Jerusalem.
Senior Palestinian negotiator Saeb Erekat said Israel's move constituted "deliberate sabotage" of Trump's efforts to restart peace talks.