Israeli forces are searching for a soldier believed captured, as a 72-hour truce with Hamas in Gaza collapsed just hours after it had begun.
The soldier, named as Hadar Goldin, 23, disappeared when Israeli forces trying to destroy a militant tunnel were attacked, Israel's military said.
Two soldiers died in the firefight in the southern Gaza Strip at 06:30 GMT.
The Gaza health ministry said at least 53 people were killed by Israeli shelling shortly after the incident.
Hamas has not confirmed or denied capturing a soldier.
In 2006 Palestinian militants captured Israeli soldier Gilad Shalit and held him for five years.
He was released in November 2011 in exchange for 1,000 Palestinian prisoners.
Lt Goldin's father Simha said in a statement that the family was "confident that Israel will do everything to bring Hadar back home".
US President Barack Obama called for the militants to free the soldier.
He said he "unequivocally" condemned Hamas for capturing the soldier "minutes after a ceasefire had been announced".
At least 1,600 Palestinians, mostly civilians, have now died in the latest conflict, and 8,400 have been injured, according to Gaza's health ministry.
Sixty-one Israeli soldiers have died, as well as three civilians in Israel.
Friday's violence comes after a ceasefire brokered by the US and UN to give civilians a reprieve from the violence collapsed.
During the morning many Palestinians headed towards areas that had been heavily shelled areas to see if their homes were still intact.
But fighting then resumed, with Israel and Hamas accusing the other of breaking the ceasefire.
Gaza's health ministry said 53 Palestinians were killed and more than 200 injured in an Israeli attack near the southern town of Rafah after the ceasefire began.
Israeli foreign affairs spokesman Yigal Palmor told the BBC that Israeli forces had retaliated after being attacked in what seemed like a planned move by Hamas.
"There was a full-scale attack on an Israeli unit and this unit had to respond," he said.
Israel says its response will be "crushing".
But Hamas spokesman Fawzi Barhoun said: "The Israelis are the ones who breached the ceasefire, and the Palestinian resistance acted in a way that ensures its right of self-defence."
Another Hamas official said the announcement of the soldier's capture was "a justification for Israel retreating from the truth and a cover-up for massacres".
Analysis: Martin Patience, BBC News, Gaza
The clashes in Rafah came just four hours into what was meant be a 72-hour ceasefire, reinforcing just how difficult it is to get truces to last beyond a very short time. Both sides will have expected such violations.
While it held, much of Gaza was relatively quiet compared to the violence in recent weeks. The streets were slowly returning back to life as shops began to reopen. People had been taking the opportunity to stock up on much-needed supplies.
A steady stream of cars headed towards evacuated neighbourhoods close to the Israeli border. People here want to see if their houses are still standing and to try to salvage what's left of their belongings.
Analysis: Bethany Bell, BBC News, Jerusalem
The news that an Israeli soldier appears to have been captured by Palestinian militants in Gaza has caused deep concern in Israel. Military service is compulsory for most people and the sense of solidarity and sympathy with the armed forces is strong; the case of Gilad Shalit was a national trauma.
He was eventually freed in 2011 when Israel authorised the release of more than 1,000 Palestinian prisoners in exchange. The government's readiness to make deals is both a strength and a weakness. It reassures Israeli soldiers and their families that the country will do what it can to secure their release.
But critics both at home and abroad say the policy makes Israel vulnerable to future attacks. Its enemies, including Hamas and Hezbollah, know that Israel is prepared to pay a very high price for the freedom of its citizens.
In other developments:
- The UN also demanded Lt Goldin's "immediate and unconditional release" and that both sides return to the ceasefire
- Palestinian and Israeli delegations arrived in Cairo, Egypt, with the hope of negotiating a longer-term cessation of hostilities, but Egyptian officials said the talks had now been postponed
- Two Palestinians have been killed in clashes with Israeli security forces in the West Bank
The latest conflict comes after the abduction and killing of three Israeli teenagers in June, blamed by Israel on Hamas, which denied being behind the killings.
Tensions rose further after the suspected revenge killing of a Palestinian teenager in Jerusalem on 2 July, after which six suspects were arrested.
After a series of Israeli air strikes in which several members of Hamas' armed wing were killed, Hamas claimed responsibility for firing rockets out of Gaza for the first time in 20 months.
The next day, Israel launched Operation Protective Edge, which it said was aimed at stopping rocket attacks and destroying Hamas' capabilities.
Are you in Gaza or Israel? Have you been affected by the violence? You can send us your views and experiences by emailing email@example.com using the subject line "Gaza Israel". If you are willing to feature in an interview, please ensure you include your contact details and a photograph of yourself to help us illustrate the story.