On Sunday afternoon, Hamas spokesman Sami Abu Zuhri said in an emailed press statement that Hamas and the Palestinian factions agreed to accept the UN-proposed ceasefire for 24 hours, but Israel rejected it.
"Hamas doesn't seek a ceasefire, but we demanded a humanitarian ceasefire for our people in the Gaza Strip," said Abu Zuhri. Witnesses said militants from Gaza and Israeli ground forces exchanged fire in eastern Gaza city.
Israeli Prime Minister Benjamin Netanyahu on Sunday accused Hamas of violating a ceasefire it had called for itself and pledged to do whatever must be done to protect his country.
In an interview with CNN, he also brushed aside allegations that Israeli forces targeted civilians in the offensive against the Gaza Strip, and blamed Hamas for using local people as "human shields."
"They are violating their own ceasefire. Under these circumstances, Israel will do what it must do to defend its people," Netanyahu vowed.
Israel had endorsed an Egypt-brokered ceasefire plan, which was rejected by Hamas, which said the truce deal did not meet some of its key demands in an acceptable proposal.
Netanyahu told CNN that Israeli forces will keep on with its military campaign in a bid to dismantle Hamas' cross-border tunnel network, and to eliminate its rocket arsenal.
"I'm not going to talk about specific military operation ... Israel is doing what any other country would do and the U.S. would do if any percent of your country were under fire and you have 60 or 90 seconds to get to a bomb shelter," the prime minister said.
"I would say we want to stop firing rockets for sure. We want to dismantle the tunnel, the terror tunnel network we uncovered. I don't know if we'll have 100 percent success," he added. "Our soldiers are dealing with it now."
In another interview with CBS, Netanyahu stressed that his country does not deliberately target civilian Gazans, and slammed Hamas for provoking conflict in residential areas, adding that his long-term goal was to avert future attacks on Israel.
The Israeli army on Sunday also denied that it was responsible for the deaths of 16 Palestinians during Thursday's attack on a UN school in northern Gaza.
"The inquiry as well as documented footage conclude that a single errant mortar landed in the courtyard of the (United Nations Relief and Works Agency for Palestine Refugees) UNRWA school in Beit Hanun when it was completely empty," an Israel Defense Forces (IDF) spokesperson said on Sunday.
The army said the findings are a result of a "comprehensive inquiry" of the events on Thursday, in which Hamas militants fired anti-tank missiles at IDF troops near the school and the IDF responded by firing mortars. Some 16 people, mostly women and children, were killed in the school and dozens wounded.
"The IDF stresses it does not operate or target international organizations in the Gaza Strip," the spokesperson added.
The UN Security Council on Monday called for an immediate humanitarian ceasefire in Gaza to allow for urgent aid to reach civilians.
The 15-member council released a statement shortly after midnight Sunday calling for the truce during the Muslim Eid festival marking the end of Ramadan.
The council expressed "strong support" for an "immediate and unconditional humanitarian ceasefire," and urged all sides to accept and fully implement the truce.
It voiced "grave concern regarding the deterioration in the situation as a result of the crisis related to Gaza and the loss of civilian lives and casualties."
Palestinian representative to the United Nations, Riyad Mansour, expressed disappointment with the statement, saying it fell short of a formal resolution demanding that Israel withdraw its forces from the Gaza Strip.
"They should have adopted a resolution a long time ago to condemn this aggression and to call for this aggression to be stopped immediately," said Mansour after the meeting.
"We are disappointed in that sense," he said, adding that the Palestinians would continue pressing the Security Council to move toward a formal binding resolution.