Hamas officials said they were not consulted before the plan was announced and charged that it failed to adequately address their demand to lift border closures imposed by Egypt and Israel.
The renewed rocket fire drew a sharp rebuke from Secretary of State John Kerry, who canceled a planned trip to Cairo.
"I cannot condemn strongly enough the actions of Hamas in so brazenly firing rockets in multiple numbers in the face of a goodwill effort to offer a cease-fire in which Egypt and Israel have joined together," he said.
The quick unraveling of the cease-fire plan underlined the lack of trust between Hamas and the Egyptian government under President Abdel-Fattah el-Sissi, who has taken a hostile stance toward the Islamist group and its backer, the Muslim Brotherhood in Egypt.
The previous Egyptian president, Mohammad Morsi, an Islamist from the Muslim Brotherhood who was deposed by el-Sissi, successfully mediated a cease-fire that ended a previous round of fighting between Israel and Hamas in 2012.
The Israeli military held fire Tuesday morning after Israel's security cabinet accepted the Egyptian plan. But Prime Minister Benjamin Netanyahu ordered renewed airstrikes six hours later after dozens of rockets and mortar rounds were fired at Israel.
"Hamas chose to continue this battle and it will pay a price for this decision," Netanyahu said. "Hamas leaves us no choice but to broaden and intensify the campaign against it."
The cease-fire proposal called for a halt to hostilities on Tuesday, followed by indirect truce negotiations in Cairo 48 hours later. The proposal said Gaza border restrictions would be lifted, subject to stabilization of the security situation on the ground.
The Qassam Brigades, the armed wing of Hamas, emphatically rejected the truce plan, calling it "an initiative of kneeling and submission." It promised that its battle with Israel would "increase in ferocity and intensity."
Hamas spokesmen sharply criticized the Egyptian cease-fire plan, charging that it had been hatched in advance with Israel.
"They presented an initiative through the media," said Sami Abu Zuhri, a Hamas spokesman in Gaza. "Nothing was presented to us, there was no consultation with us about anything, so no one has the right to demand that we commit to anything. . . . This policy of pressure is unacceptable."
Moussa Abu Marzouk, a top Hamas official, told the Lebanese TV channel Al Mayadeen: "The siege on Gaza must be broken and the people of Gaza should live freely like other people of the world."
The opening of Gaza border crossings is a critical issue for Hamas, which has suffered a financial crisis since Egyptian forces shut down smuggling tunnels to Gaza _ a major source of income for the militant group _ and kept the Rafah border crossing to Egypt largely closed.
"The devil is in the details," Osama Hamdan, the Hamas representative in Lebanon, said in an interview with the BBC and Al Jazeera English television. "They tried to put the carriage in front of the horse. They wanted first to have a cease-fire and then let's discuss the details, which will not work."
Kerry said he hoped Egypt would be able to "leverage" Hamas into agreeing to the cease-fire plan. The Obama administration has been hampered in its attempts to promote a cease-fire by its boycott of Hamas, which it considers a terrorist organization. Instead it has prodded Egypt to take a more prominent mediating role.
Suggesting that Hamas' military leaders were setting the group's policy, Kerry said he hoped the political leadership of Hamas would prevail on its armed wing to end the hostilities.
Israel's agreement to a cease-fire caused strains in Netanyahu's governing coalition, where rightist ministers and hawkish members of the prime minister's Likud party have urged even tougher military action against Hamas. As the rocket attacks continued on Tuesday, the outspoken foreign minister, Avigdor Lieberman, called for a reoccupation of the Gaza Strip.
In response, Netanyahu sacked Deputy Defense Minister Danny Danon, a Likud member who had accused the prime minister of showing "weakness" in his policy toward Hamas. Netanyahu said that Danon's criticism in the midst of a military campaign was "irresponsible," and he accused him of serving Hamas "as a tool to attack the government."
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