The speedy resumption of violence, less than a day after Egypt presented its cease-fire plan, illustrated that it will be harder than in the past to negotiate an end to Israel-Hamas fighting. A key difference to a previous truce in 2012 is that Hamas does not trust the current rulers of Egypt who deposed a Hamas-friendly government in Cairo a year ago.
Gaza militants fired close to 100 rockets since the morning, when the truce was to have begun, the Israeli military said. In the evening, a quick barrage of 40 rockets fell over the course of a few minutes. Israeli medics said two people were injured, one seriously. Palestinian health officials say 194 Palestinians were killed and more than 1,400 over the past week.
Hamas believes it has little to lose by continuing to fight, while a truce on unfavorable terms could further weaken its grip of the Islamic group on the Gaza Strip, a territory it seized in 2007.
The Egyptian plan asked both sides to halt hostilities without preconditions and then to try to negotiate a new border regime easing the blockade of Gaza, with Cairo's mediation.
Hamas wants a significant easing of the blockade, enforced by Israel and Egypt by varying degrees since 2007. Egypt tightened the closure over the past year by shutting down smuggling tunnels that were crucial for Gaza's economy, pushing Hamas into a severe financial crisis.
"The siege on Gaza must be broken and the people of Gaza should live freely like other people of the world," Moussa Abu Marzouk, a top Hamas official, told the Lebanese TV channel Al-Mayadeen. "There should be a new equation so that we will not have a war on Gaza every two years."
Israel wants a deal that will ensure a halt to rocket fire from Gaza, but it is not clear what concessions it might be willing to make to Hamas on easing the closure.
Israel agreed to the Egyptian plan, proposed late Monday, and for about six hours Tuesday complied with an Egyptian call for de-escalation. But after the continued rocket fire from Gaza, Israel resumed air strikes at its previous heavy pace.
After the renewed rocket fire from Gaza, Israeli Prime Minister Benjamin Netanyahu and Defense Minister Moshe Yaalon "directed the military to act with intensity against terror targets in Gaza," said an Israeli official who spoke on condition of anonymity because he was not authorized to discuss the decision with the media.
A senior Israeli military official suggested the Egyptian plan hadn't collapsed entirely.
He said that even though Israel resumed bombing Gaza, it would stop if Hamas accepts the truce and that the coming hours are critical. If not, the military has a plan in place to significantly amp up its offensive, including a possible ground operation, said the official who spoke on condition of anonymity because he was discussing military strategy.
Israel has warned in the past that it might launch a ground of offensive in Gaza and has amassed thousands of troops on Gaza's border. However, entering Gaza would likely drive up casualties on both sides. Israel has often hesitated in the past to embark on ground operations for fear of getting entangled in the densely populated territory of 1.7 million.
The outbreak of cross-border fighting, which began July 8, has been the deadliest round since a major Israeli military offensive in the winter of 2008-2009. The previous outbreak of cross-border violence, in 2012, eventually ended with the help of Egypt, at the time seen as a trusted broker by Hamas.
Hamas officials on Tuesday rejected the current Egyptian plan as is, noting they weren't consulted by Cairo. Some portrayed the truce offer as an ultimatum presented to Hamas by Israel and Egypt.
The officials said the Egyptian plan offered no tangible achievements, particularly on easing the border blockade.
Osama Hamdan, a senior aide to top Hamas leader Khaled Mashaal, said the movement needs detailed assurances that Gaza's borders will be opened, particularly the Rafah crossing between Gaza and Egypt, the territory's main gate to the world.
Hamas also wants to be recognized by Egypt as a partner in any truce efforts.
Mushir al-Masri, a Hamas leader in Gaza, said the movement wants additional mediators and international guarantees of any deal.
"Mediation to end this aggression needs to come from different countries, and the guarantees should be given by different countries in order to commit the occupation (Israel) to what any future agreement might say," al-Masri said, without naming preferred brokers.
Qatar and Turkey, seen as more sympathetic to Hamas, have been involved behind the scenes, but it's not clear to what extent. The emir of Qatar visited Turkey on Tuesday for talks with Turkish leaders.
Palestinian President Mahmoud Abbas, Hamas' main political rival, was to meet in Cairo on Wednesday with Egyptian President Abdel-Fattah el-Sissi, and then fly to Turkey for high-level talks.
Before the outbreak of the latest round of fighting, Abbas had reached a tentative unity deal with Hamas that would have given him a new foothold in Gaza. However, a significant easing of the Gaza blockade in a truce deal would revitalize Hamas, make it less dependent on Abbas and possibly scuttle the unity agreement.
Meanwhile, Israel won diplomatic points for accepting Egypt's plan.
In Vienna, Secretary of State John Kerry blasted Hamas for firing rockets after the proposed cease-fire was to have taken effect.
"I cannot condemn strongly enough the actions of Hamas," Kerry told reporters. In contrast, he praised Egypt's intervention and Israel's acceptance of the deal.
Kerry said the U.S. would continue pushing for a cease-fire is because of the potential for the violence escalating even further.
Associated Press writers Tia Goldenberg and Aron Heller in Jerusalem, and Zeina Karam in Beirut contributed reporting.