The threat of a renewed escalation in attacks came as Washington's top diplomat, Secretary of State Antony Blinken, met officials in Israel to seek a longer pause in the devastating war.
The fate of the truce is hanging in the balance once again.
A Hamas source told AFP that 10 more Israeli captives would be released from Gaza in exchange for Palestinian prisoners held by Israel, after the warring parties agreed to extend the pause in combat operations until Friday morning.
"All of them are alive," said the source who is not authorised to speak to the media and asked to remain anonymous. "Israel last night refused a list Hamas proposed that included three Israeli bodies."
Only hours after the truce extension, the Islamist militants claimed responsibility for a shooting in Jerusalem that killed three people and called for an "escalation of the resistance".
The morning attack saw two gunmen from annexed east Jerusalem kill three people and wound eight others at a bus stop in the western part of the city, before two off-duty soldiers "neutralised" them, police said.
Ten captives per day
Separately, two Israeli soldiers were slightly injured in a ramming attack on a checkpoint in the occupied West Bank on Thursday, the army said, adding the assailant had also been "shot and neutralised".
If the truce does come to an end on Friday, it will be despite international pressure for more time to allow medical supplies, food and fuel into the besieged Gaza Strip after fierce combat and bombardments sparked by Hamas's bloody October 7 attacks on Israel.
"We have seen over the last week the very positive development of hostages coming home, being reunited with their families," Blinken said at a meeting with Israeli President Isaac Herzog in Tel Aviv.
"It's also enabled an increase in humanitarian assistance to go to innocent civilians in Gaza who need it desperately. So this process is producing results. It's important, and we hope that it can continue."
Blinken later told Israeli Prime Minister Benjamin Netanyahu it was "imperative" to protect civilians in southern Gaza "before any military operations there".
The latest extended truce had been due to end at 0500 GMT, but the Israeli army said the "operational pause" would continue as international mediators negotiate the release of hostages held by Hamas.
Qatar, which has led the truce negotiations supported by Egypt and the United States, confirmed the pause had been extended for one day "under the same previous conditions".
Fighting began on October 7 with Al-Aqsa Flood operation by Hamas, killing 1,200 people, mostly civilians, and capturing about 240, according to Israeli authorities.
In response, Israel unleashed an air and ground military campaign that the Hamas government says has killed more than 15,000 people in Gaza, more than two third of them women and children.
The truce agreement allows for extensions if Hamas can continue to release 10 captives per day, but both sides have warned they are ready to return to fighting.
Shortly after the hostages arrived in Israel, the country's prison service said 30 Palestinian prisoners had been released, including well-known activist Ahed Tamimi.
Since the truce began on November 24, 70 Israeli captives have been freed in return for 210 Palestinian prisoners.
At least 24 foreigners, most of them Thais living in Israel, have been freed outside the terms of the deal.
Israel says it sees the truce as a temporary halt intended to free captives, but there are growing calls for a more sustained pause in fighting.
Israel's army has said it is investigating a claim by Hamas's armed wing that a 10-month-old baby captive, his four-year-old brother and their mother had been killed by Israeli bombing in Gaza.
Before the truce Israeli ground and air forces had pounded Gaza, forcing an estimated 1.7 million people -- around 80 percent of the Hamas-run territory's population -- to leave their homes and limiting the entry of food, water, medicine and fuel.
'Everything is gone'
Conditions in Gaza remain "catastrophic", according to the World Food Programme, and the population faces a "high risk of famine".
The truce has allowed some of the displaced to return to their homes, but for many there is little left.
"I discovered that my house had been completely destroyed -- 27 years of my life to build it and everything is gone," said Taghrid al-Najjar, 46, after returning to her home in southeastern Gaza.
The Israeli war on Gaza has also raised tensions in the West Bank, where nearly 240 Palestinians have been killed by either Israeli soldiers or settlers since October 7, according to the Palestinian health ministry.
That figure exceeds the entire toll in the Israeli-Palestinian conflict for all of last year when 235 people died, mostly Palestinians, an AFP tally showed.
An eight-year-old boy and a teenager were the latest deaths in the occupied territory, with Israel saying its troops "responded with live fire" after suspects hurled explosive devices.
On Thursday, two gunmen from east Jerusalem killed three people and wounded eight others at a bus stop in the western part of the city before two off-duty soldiers "neutralised" them, police said.