The Israeli officer, known only as Lt-Col M, was killed and another soldier wounded in an undercover operation.
According to the Qassem Brigades, the armed wing of Hamas, the Israelis had penetrated two miles into Gaza in a civilian vehicle before they were discovered.
Witnesses reported tank fire and air strikes in what the IDF described as “an exchange of fire”.
The IDF said the force had “acted with bravery and determination. The purpose of the operation was not to kill or abduct.”
Such missions were launched “only after serious deliberations, which often remain classified.”
At today's funeral, Israel's president Reuven Rivlin, hugged the officer's children, telling them, "your dad was a hero, the greatest hero".
He was one of "one of the bravest and most daring soldiers and commanders of the state of Israel and he fell defending the citizens of Israel.
The latest clash comes despite efforts in recent months by Egypt to broker a truce between Israel and Hamas.