The Israeli military said the body was being taken for formal identification.
Earlier, Netanyahu had said that Israel was about to receive the body of Hadar Goldin, who was killed in a Hamas attack during the previous conflict in 2014 and whose body had been held in Gaza ever since.
Hamas's armed wing also said on Sunday that it would hand over Hadar Goldin's body.
If the body is confirmed to be that of Lieutenant Goldin, Hamas will return all 20 living hostages and the bodies of 24 of the 28 dead hostages as part of the first phase of a ceasefire deal.
Netanyahu said Lieutenant Goldin's family would now be able to bury him according to Jewish customs and reiterated his intention to bring back the bodies of all the dead hostages.
"We have brought back 250 bodies so far. We will bring them all back," he said.
On Saturday, Lieutenant Goldin's family said, "The whole country is waiting for Hadar to come home."
"We are waiting for official confirmation that Hadar has returned to Israel," the family said in a statement. "We never leave anyone behind in this country. We ask everyone to remain calm. It's not over until it's over."
Lieutenant Goldin, from Kfar Saba, was the only dead hostage whose remains were held in Gaza before the Hamas-led attack on Israel on October 7, 2023, which triggered the current war.
He was killed in fighting on August 1, 2014, shortly after a ceasefire began in the war between Israel and Hamas that year. He was among a group of Israeli soldiers patrolling an agricultural area near Rafah in southern Gaza when they were attacked by a group of Hamas fighters.
The Israeli military determined that Lieutenant Goldin, along with two other soldiers, had been killed in the exchange of fire, and that his body had then been dragged into an underground tunnel by Hamas fighters.
The Israeli military launched heavy shelling to prevent Hamas from taking Lieutenant Goldin hostage. The bombardment of Rafah continued for four days, even after Lieutenant Goldin was declared dead, killing many Palestinian civilians.
On Saturday, the Israeli military said it had identified a body handed over from Gaza as that of Israeli-Argentinian Lior Rudaeff.
Also on Saturday, two Palestinians were killed by Israeli fire in Gaza. The Israeli military said the two men had crossed the yellow line marking the Israeli-controlled boundary in Gaza and were posing an "immediate threat."
According to the Hamas-run health ministry, whose figures the United Nations considers reliable, at least 241 people have been killed in Israeli military operations since the ceasefire began.
The Israeli military launched an operation in Gaza in response to the October 7, 2023 attack, in which Hamas-led gunmen killed approximately 1,200 people in southern Israel and took 251 others hostage.
The health ministry reports that at least 69,169 people have been killed in Israeli attacks in Gaza since then.