The apparent capture of the soldier and the collapse of the truce set the stage for a possible expansion of Israel's 25-day-old military operation against Hamas.
US President Barack Obama and UN chief Ban Ki-moon called for the immediate release of the soldier but also appealed for restraint. In Israel, senior Cabinet ministers convened late Friday in a rare emergency meeting after the start of the Jewish Sabbath.
The search for the missing soldier centered on the outskirts of the town of Rafah, on the Egypt-Gaza border.
At least 140 Palestinians were killed Friday in Gaza, with at least 70 killed in the Rafah area along with two Israeli soldiers.
Earlier Friday, Israel and Hamas accused each other of breaking the truce, which had been announced by the US and the UN, and took effect at 8am.
Palestinians return to the heavily bombed Gaza City neighborhood of Shijaiyah, close to the Israeli border. (AP photo)
The breakdown meant there would be no reprieve for the 1.7 million residents of Gaza, where large parts have been devastated by airstrikes and shelling, and at least 1,600 people - mostly civilians - have been killed and more than 8,000 wounded. Israel has lost 63 soldiers and three civilians.
The fighting in the Rafah area continued into the night, with residents reporting airstrikes along the Egypt-Gaza frontier as well as heavy tank and artillery shelling. The Israeli military said it was searching for the missing soldier and had sent automated calls or text messages to Rafah residents to stay indoors.
"We are under fire, every minute or so tanks fire shells at us," said Rafah resident Ayman Al-Arja. "I have been thinking of leaving since 2pm, but tank fire can reach anywhere, and I was scared they will hit my pickup truck. Now we are sitting in the stairwell, 11 members of my family, my brother, his nine children and wife. We just have water to drink and the radio to hear the news."
The 45-year-old Al-Arja added: "We are just staying put waiting for God's mercy."
The heavy shelling in Rafah was part of operational and intelligence activity to locate the missing officer, 2nd Lt. Hadar Goldin, the Israeli military said.
An hour after the cease-fire began, gunmen emerged from one or more Gaza tunnels and opened fire at Israeli soldiers, with at least one of the militants detonating an explosives vest, said Israeli army spokesperson Lt. Col. Peter Lerner.
Goldin, a 23-year-old from the central Israeli town of Kfar Saba, was apparently captured in the ensuing mayhem, while another two Israeli soldiers were killed.
"We suspect that he has been kidnapped," Lerner said.
Watch: Gaza ceasefire collapses, fresh fighting erupts
Obama called for Goldin's unconditional and immediate release and said it would be difficult to put the cease-fire back together. However, he said the US will continue working toward a ceasefire.
He said Israel committed to the truce, but at the same time called the situation in Gaza "heartbreaking" and repeated calls for Israel to do more to prevent Palestinian civilian casualties.
"Innocent civilians caught in the crossfire have to weigh on our conscience, and we have to do more," Obama said. He added that Israel must be able to defend itself, but that irresponsible actions by Hamas have put civilians in danger.
Israel has gone to great lengths in the past to get back its captured soldiers. In 2011, it traded hundreds of Palestinian prisoners for an Israeli soldier who had been captured by Hamas-allied militants in 2006. The capture of two soldiers in a cross-border operation by Lebanon's Hezbollah guerrillas in 2006 sparked a 34-day war between the Iranian-backed Shiite group and Israel.
A Hamas spokesperson, Fawzi Barhoum, would neither confirm nor deny the capture, saying the event was being used - along with the killing of two Israeli soldiers in the Rafah area - as a cover for what he called a "massacre" in Rafah.
The violence killed at least 70 Palestinians and wounded 440 in the Rafah area, according to Gaza Health Ministry official Ashraf al-Kidra. The dead included paramedic Assef al-Zamily, killed when an Israeli tank shell hit an ambulance in which he was riding, al-Kidra said.
Another 70 Palestinians were killed elsewhere in Gaza on Friday, according to al-Kidra.
Ban blamed Hamas for violating the cease-fire and demanded the immediate and unconditional release of Goldin.
The UN chief also urged both sides "to show maximum restraint and return to the agreed 72-hour humanitarian cease-fire that tragically lasted such a brief period of time," UN spokesperson Stephane Dujarric said.
Israeli Prime Minister Benjamin Netanyahu told U.S. Secretary of State John Kerry by phone that Palestinian militants had "unilaterally and grossly" violated the cease-fire and attacked Israeli soldiers after 9am.
"Israel will take all necessary steps against those who call for our destruction and perpetrate terrorism against our citizens," Netanyahu told Kerry, according to a statement from the prime minister's office.
Moussa Abu Marzouk, Hamas' deputy leader, denied that Hamas violated the truce. He told Al-Arabiya news channel from Cairo that the movement's military wing carried out no military operations after 8am.
A longtime friend of Goldin's said he is engaged to get married and that he studied at a Jewish seminary in the West Bank settlement of Eli. Goldin has a twin brother who also is in the military on the Gaza front lines, said the friend, who spoke on condition of anonymity because he did not have the family's permission to discuss Goldin's personal details with the media.
The soldier's father, Simha Goldin, is a Tel Aviv University professor specializing in Ashkenazi Jewry, the friend said.
"We want to support the military in the fighting against Hamas in Gaza. We are sure the military will not stop before it turns over every stone in Gaza and returns Hadar home safe and sound," the father said in a statement to reporters outside his home.
The shelling in Rafah sent families fleeing from apartment blocks. One woman carrying two children rushed toward a parked car, yelling to a bystander, "Quick, open the car door!"
Ambulances ferried the wounded to al-Najar hospital, where family members frantically searched for loved ones among the bloodied bodies on stretchers. Many of the wounded were children. In one room, four children were treated on a single bed, while others were examined on the floor.
On July 8, Israel began an aerial campaign against Gaza aimed at halting Palestinian rocket fire and later sent in ground troops to target launch sites and tunnels used by Hamas to carry out attacks inside Israel.
Israeli soldiers of the 155mm artillery cannons unit fire towards the Gaza Strip from their position near Israel's border with the coastal Palestinian enclave. (AFP Photo)
Four brief humanitarian cease-fires were announced, but each broke within a few hours.
The Israeli military said Gaza militants fired at least 38 rockets and mortars at Israel since the start of Friday's cease-fire, and two were intercepted.
The latest ceasefire, announced by Kerry and Ban, was intended to be the first step toward a lasting truce, with Egypt inviting Israeli and Palestinian delegations to Cairo for talks. Despite its collapse, an Egyptian government official said Cairo had not canceled its invitation for Palestinians and Israelis to hold talks.
The official spoke on condition of anonymity because he wasn't authorized to talk to the media.
Soon after the cease-fire started, Gaza's residents took advantage of the lull to return to their homes, many of which had been destroyed. In the heavily bombarded Gaza district of Shijaiyah, less than 1.6 kilometers (a mile) from the Israeli border, residents surveyed the damage.
Bassem Abul Qumbus found that his three-story home - in which he had invested tens of thousands of dollars - had been shattered. Shells had punched a hole in the ceiling of one bedroom and a wall had collapsed into the kitchen.
"The work of all those years is gone," he said as he struggled to salvage flour from bags that had been torn apart by shrapnel.
In the southern town of Khan Younis, residents searched for bodies amid destroyed homes. Rescuers and volunteers used makeshift stretchers to carry away corpses, some badly burned.
Read: Gaza people say war must go on
Nidal Abu Rjeila found the body of his disabled sister on the side of the road, her wheelchair flipped upside down. He said her body had been there for five days.
"I tried to reach human rights groups and the Red Cross, but no one was answering me," he said, overcome by grief.
Israel says it has tried to spare civilians by warning them before military strikes, and that Hamas endangers Gazans by firing rockets from residential areas.
Palestinian militants have shot hundreds of rockets into Israel during the conflict, extending their reach to major cities but causing few casualties, in part because Israel's "Iron Dome" defense system has intercepted many of the missiles.
Hamas has vowed to keep fighting until Israel and Egypt lift a crippling blockade of Gaza imposed after the Islamic militant group seized power there in 2007.
Full coverage: Gaza under attack