The al-Qassam Brigades, the military wing of Hamas, has denied capturing a missing Israeli soldier after Barack Obama, the US president, called for his release as a precondition for further ceasefire talks.
Obama made the comments at a White House news conference on Friday, after a UN and US-brokered 72-hour truce between Israel and Hamas broke down just hours after coming into effect.
The Israeli army said Hadar Goldin, 23, went missing when its soldiers, two of whom were killed, were attacked while trying to destroy a Hamas tunnel in southern Gaza.
"If they are serious about trying to resolve this situation, that soldier needs to be unconditionally released as soon as possible," Obama said.
The al-Qassam Brigades said: "We have no idea about where the Israeli soldier is or what is the situation.
"We lost contact with the group who made the suicide mission near Rafah after it was done. And we believe everyone in this group was killed by an Israeli air strike including the Israeli soldier who the Israelis are talking about having disappeared."
The UN also called for the release of Goldin. In a statement, a spokesman for Ban Ki-moon, said: "The [UN] secretary-general demands the immediate and unconditional release of the captured soldier."
Obama blamed Hamas for breaking the ceasefire, while Hamas said that Israeli forces were conducting operations east of Rafah after the ceasefire went into effect.
Renewed Israeli shelling killed more than 80 Palestinians on Friday. Fifteen of those victims, including five children aged 3 to 12, came from the same family whose house was destroyed.
The Palestinian Ministry of Health said nearly 400 people were injured in three Israeli air strikes on Rafah in the south of the Gaza Strip.
Meanwhile, in a show of support for Israel, the US Congress overwhelmingly passed a $225m package to replenish Israel's missile defence system.
The House's 395-8 vote in favour of the measure followed Senate approval earlier on Friday. The bill now goes to Obama for his signature.
Speaking at Friday's news conference, Obama also said it would be difficult to achieve a ceasefire in Gaza after the latest truce fell apart but strongly defended US Secretary of State John Kerry over his failed diplomatic drive.
Kerry came under heavy criticism in Israel earlier this week for his latest attempt at a ceasefire after some Israelis viewed his bid for an immediate pause in fighting as basically trying to stop Israel from dismantling Hamas tunnels.
"When I see John Kerry going out there and trying to broker a ceasefire, we should all be supporting him," Obama said.
"There shouldn't be a bunch of complaints and second-guessing about, 'well, it hasn't happened yet,' or nitpicking before he's had a chance to complete his efforts."
The Israeli-Palestinian conflict has tested US diplomacy and laid bare the limits of Obama's ability to influence events in the Middle East.
An ABC News/Washington Post poll this week said 39 percent of Americans approve of Obama's handling of the situation in Israel and Gaza while more than half, 52 percent, disapprove.
Gaza officials say at least 1,635 Palestinians, mostly civilians, have been killed and 8,840 wounded.
|INTERACTIVE: Gaza Under Attack
Sixty-three Israeli soldiers have been killed and more than 400 hurt. Three civilians have been killed by Palestinian rockets in Israel.
Egypt, which invited the Israeli government and the Palestinian Authority to come to Cairo for longer-term truce talks, reiterated later on Friday its invitation to Israeli and Palestinian delegations, saying it is "still in place" despite the 72-hour humanitarian truce breaking down.
Palestinian President Mahmoud Abbas said a joint Palestinian delegation, including Hamas and Islamic Jihad, would travel to Cairo on Saturday for ceasefire talks, despite the renewed fighting in Gaza.
However, Jeffrey Feltman, the UN Under Secretary-General for Political Affairs, said: "The chance for success of these talks rested on quiet, rested on the 72-hour ceasefire.
"Right now we have escalation. I myself have a hard time envisaging how these talks would work right now."