Israel has denied Hamas' claim of capturing Israeli soldier during the deadliest day yet of fighting in Gaza.

Hamas' military wing said Sunday it had taken the soldier during an early morning operation.

But Ron Prosor, the Israeli ambassador to the United Nations, later dismissed the claim.

"There's no kidnapped Israeli soldier, and those rumors are untrue," he told reporters at the United Nations in New York.

Abu Obeida, a spokesman for Hamas' military wing, had earlier provided the supposed soldier's name and ID, saying, "He is a prisoner, and if Zionists lie about the dead and wounded, then the fate of this soldier is their responsibility."

Gunfire and cheers erupted in Gaza on Sunday in apparent celebration of the alleged capture of the soldier, according to CNN reporters on the ground.

Hamas' claims stirred memories of militants' abduction of the Israeli soldier Gilad Shalit in 2006. He was released some five years later in exchange for more than 1,000 Palestinian prisoners.

The death toll from the Gaza conflict climbed sharply after Israel's assault Sunday on the town of Shaja'ia near Gaza City, which sent hundreds of panic-stricken people fleeing into Gaza City.

Scores of Palestinians were killed during heavy shelling of Shaja'ia, bringing the total number killed since the start of Israel's military operations against Hamas to 501, according to the Gaza Health Ministry. More than 3,000 have been wounded.

Extensive fighting continued in Shaja'ia overnight into Monday, the Israeli military said.

Hamas spokesman Sami Abu Zuhri, speaking to Al-Jazeera, said that Israel committed "a crime against humanity," and that most of those killed in Shaja'ia were women and children.

The Israeli military said it had warned residents days in advance to leave Shaja'ia, which it described as a key area that Hamas uses to launch rockets into Israel. It accused Hamas of ordering people to stay in the area.

Israel said 13 soldiers were killed Sunday, bringing the total killed during the Gaza conflict to 18, in addition to two civilians. At a news conference, Israeli Prime Minister Benjamin Netanyahu expressed the country's "deep pain" at the loss of the soldiers.

Hamas claimed responsibility for their deaths, calling it a "heroic operation."

Among those killed were Max Steinberg, a California native, and Sean Carmeli, an IDF soldier from South Padre Island, Texas, the U.S. State Department said.

"We're doing everything we can not to harm the people of Gaza," Netanyahu said. "Hamas is doing everything they can to make sure the people of Gaza suffer."

But people in Gaza who spoke with CNN described a different situation.

"Nobody is safe and nobody can flee anywhere because everywhere is targeted," said Enas Sisisalem, a mother of two who lives in the al-Remal neighborhood of Gaza City. "When we hear the shelling my kids will cry."

She said she had seen people running away from Shaja'ia.

"The shelling did not stop all night or morning," Sisisalem said Sunday. "The people ran away from their houses with their clothes and kids only, barely grabbing anything with them."

The United Nations has estimated that around 70% of the Palestinian killed in Gaza have been civilians.

(CNN)