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An Israeli fire killed at least two people in Rafah and injured three others in Khan Younis in the south of Gaza, raising fear among Palestinians that the ceasefire could collapse altogether after Israel imposed a total blockade on the area.
A first phase of a ceasefire that began in January ended over the weekend with no agreement on what will happen next.
Hamas say an agreed second phase must now begin, leading to a permanent Israeli withdrawal and an end to the war. Israel has instead offered a temporary extension into April, with Hamas to release more hostages in return for Palestinian detainees, without immediate talks on Gaza's future.
Two Israeli government officials said mediators had asked Israel for a few more days to resolve the standoff over the ceasefire.
Israel raised the stakes on Sunday by imposing a total blockade on all supplies, including food and fuel, to sustain the 2.3 million Gazans living among the ruins.
Hundreds of lorries carrying supplies were backed up in Egypt, denied permission to enter. Gaza residents said shops had been swiftly emptied of all supplies and the price of a sack of flour had more than doubled overnight.
Residents of the enclave said Israeli tanks stationed near the eastern and southern borders of Gaza intensified gunfire and tank shelling into the outskirts throughout the night, raising fears among the population that fighting could resume.
At least two people were killed by an Israeli drone fire in Rafah, and three people were wounded by a helicopter that fired on Khan Younis, medics said. The Israeli military made no immediate comment.
A Palestinian official with one of the groups allied to Hamas in Gaza told Reuters a state of alert had been declared among fighters in anticipation of any "treacherous move by the occupation".
Israeli Prime Minister Benjamin Netanyahu's office said it had adopted a proposal by US President Donald Trump's envoy, Steve Witkoff, for a temporary ceasefire for the Muslim holy month of Ramadan and Jewish feast of Passover, ending around April 20.
The truce would be conditional on Hamas releasing half of the remaining living and dead hostages on the first day, with the remainder released at the conclusion if an agreement is reached on a permanent ceasefire.
Hamas says it is committed to the originally agreed ceasefire that had been scheduled to move into a second phase, with negotiations aimed at a permanent end to the war, and hostages could be released only under that plan.
Meanwhile, the Hamas-run Gaza interior ministry called on residents to provide information about merchants raising food prices in the wake of the new blockade.
Tamer al-Burai, a Gaza businessman, said that with shops suddenly empty, the price of a sack of flour had risen to 100 shekels (AED 102) from 40 shekels (AED 40). Prices for cooking oil, fuel, and vegetables had also surged.
"It is catastrophic and things might become worse if the ceasefire isn't resumed or there is no intervention by the local authorities against greedy merchants," he told Reuters via a chat app.
Salama Marouf, the head of the Hamas-run Gaza government media office, urged Gazans not to panic, saying there was enough food in markets for at least two weeks. The economy ministry was already involved in the effort to compel merchants not to increase prices.
"There are pressures to compel the occupation to commit to the ceasefire agreement and to reopen the crossing," said Marouf in a statement on Monday.
Israel's onslaught has killed more than 48,000 Palestinians in Gaza, according to local health authorities, and displaced nearly the entire population.
The war began when Hamas-led fighters attacked southern Israel on October 7, 2023, killing 1,200 people and capturing more than 250 hostages, according to Israeli tallies. Fifty-nine hostages are believed to remain in Gaza.