The president later clarified that the United States would not be involved in such an action.
It was unclear when Maj. Gen. Mohammed al-Ghomari was killed, or by whom, but Israel appeared to claim the killing.
Unresolved issues and flare-ups of violence threaten to destabilize the fragile agreement.
Ceremonies took place on Thursday to commemorate two years since the surprise attack of Oct. 7, 2023, on southern Israel.
With the bodies of 10 people returned from Gaza, Israelis elated by the release of hostages began mourning those who did not make it home alive.
The Palestinian militant group said it needed special equipment to locate and extract the remaining remains.
The militants said they would need special equipment to retrieve more bodies in Gaza. The announcement could put the truce with Israel at risk.
A video this week captured Hamas fighters in Gaza executing Palestinian rivals as the militant group tries to assert that it is still the dominant force in the territory after two years of war with Israel.
A video this week captured Hamas fighters in Gaza executing Palestinian rivals as the militant group tries to assert that it is still the dominant force in the territory after two years of war with Israel.
Hamas has handed over the bodies of eight people, but says it is struggling to find the remains of others after two years of war.