President Joe Biden and his top diplomats, including Secretary of State Antony Blinken, had sought closure during his term.
Qatari and Hamas officials say a last-minute dispute in cease-fire talks between Israel and Hamas has been resolved.
After months of deadlock, Israel and the militant group Hamas reached a fresh Gaza ceasefire and hostage release agreement.
But the extraordinary collaboration between outgoing and incoming presidents did not stop both sides from claiming credit.