GAZA CITY (CNN) -- Not long after Israel resumed its offensive in Gaza on Sunday because of "incessant rocket fire" from Gaza, Hamas said it agreed to a 24-hour U.N.-mediated cease-fire, a move that prompted the United Nations to try to get Israel to accept the hiatus.
Diplomats worked to forge what they call a "humanitarian pause" as bursts of Israeli artillery fire echoed once again across parts of the territory, alternating with periods of quiet, and rockets from Gaza flew into southern Israel.
The Israeli Security Cabinet had agreed to a U.N. request late Saturday to extend a cease-fire that started Saturday morning until midnight Sunday (5 p.m. ET Sunday) -- on the condition that its military could keep dismantling and destroying Hamas' tunnels, according to senior Israeli officials.
Hamas rejected that idea, saying it won't tolerate Israeli troops in the territory. And militants in Gaza fired mortars and rockets into Israel late Saturday and through Sunday morning, killing an Israeli soldier, the IDF said.
Israel then resumed its offensive.
"Following Hamas' incessant rocket fire throughout the humanitarian window, which was agreed upon for the welfare of the civilian population in Gaza, the IDF will now resume its aerial, naval and ground activity in the Gaza Strip," the Israeli Defense Forces said in a statement.
But Hamas, the militant group that is in control of the besieged Palestinian territory, then changed its stance.
Hamas agreed to a 24-hour U.N.-mediated "humanitarian pause" starting at 2 p.m. local time (7 a.m. ET), a text message from Hamas spokesman Sami Abu Zuhri said.
"In response to the intervention by the United Nations and taking into account the conditions of our people and the upcoming Eid holiday, an accordance has been reached between Palestinian resistance groups to call a humanitarian calm for 24 hours," Zuhri said.
U.N.: 'Please don't go back on the streets'
It is now up to Israel to decide whether it wants to accept the "humanitarian pause," according to U.N. envoy Robert Serry, who is working around the clock for a pause in violence.
"I'm extremely concerned after both rocket fire and of course also Israeli operations are continuing. And I appeal on both sides to now show utmost restraint for this humanitarian pause to become effective, I hope as soon as possible," Serry said. "This will allow civilians to resume their daily lives, both in Israel and in Gaza."
Noting that fighting persists, Serry appealed to both sides "not to miss maybe this last opportunity for calm." He urged Gazans to stay home until there's a durable cessation in violence.
Serry, a Dutch diplomat, is the U.N. special coordinator for the Middle East peace process.
"Please don't go back on the streets or to your houses now until there is an effective cease-fire and an announcement to that effect is made," he said on CNN. "It is still very dangerous for people in Gaza."
Israel launched its ground incursion in Gaza 10 days ago with the stated aim of taking out the threat posed by the tunnels, which run under the border and have been used by militants to carry out attacks on Israeli soil.
The temporary truce in the conflict -- which has killed more than 1,000 people, most of them Palestinian civilians -- had enabled medical supplies to be brought into Gaza, families to emerge from shelters and people to dig out the dead from piles of rubble.
Death toll over 1,000
The IDF said Saturday that many Gaza residents were returning to previously evacuated areas despite repeated warnings, placing themselves at risk. It said operations against the tunnel threat continued and defensive positions were being maintained.
Palestinians found more than 100 bodies in areas that have been too dangerous to enter in recent days because of Israeli bombardment, Dr. Ashraf al-Qedra from the Gaza Ministry of Health told CNN.
Nearly 1,050 Palestinians have been killed and about 6,000 wounded since the Israeli operation against Hamas in Gaza started on July 8, al-Qedra said.
The Israeli operation started with airstrikes, and a ground incursion in Gaza followed on July 17.
Israel blamed Hamas for civilian casualties resulting from Israeli strikes, saying militants have embedded themselves among the civilian population.
"The IDF targets terrorist centers, but if residents are inadvertently hit, it is Hamas which is responsible given that it has -- again -- violated the humanitarian truce that Israel acceded to," Netanyahu's media adviser said.
The IDF said Sunday that the one soldier killed overnight brought to 43 the number of Israeli troops killed in the Gaza operation. Two Israeli civilians have been killed.
CNN's Karl Penhaul reported from Gaza; Chelsea J. Carter reported and wrote from Atlanta; and Jethro Mullen reported and wrote from Hong Kong. CNN's Ray Sanchez, Yousuf Basil, Salma Abdelaziz, Ben Wedeman, Elise Labott, Richard Roth, Ian Lee,Tal Heinrich, Tim Lister and Samira Said contributed to this report.
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