Israel’s pledge to intensify its military operation in the Gaza Strip could hasten the moment when the Obama administration will be forced to decide whether to use its leverage to corral its closest ally in the Middle East.

Israeli officials, in a series of television interviews, statements and social-media venues, said Tuesday that Hamas’s rejection of a cease-fire offer validated the force it has used over eight days of conflict and made legitimate their argument for a wider military effort.

The Obama administration appeared to accept that rationale, blaming the armed Islamist movement in Gaza for missing an opportunity to end the eight-day aerial assault and avoid a ground invasion. But if the recent past is any guide, the administration will soon be under pressure from European and Arab allies to call on Israel to end the military operation.

Doing so now would be diplomatically delicate for the administration. Hamas rejected the Egyptian-negotiated cease-fire offer and continued to fire rockets into Israel on Tuesday, claiming the first Israeli life in the most recent conflict.

But a broader Israeli operation and an attendant spike in Palestinian casualties could quickly add pressure on the Obama administration to demand an end to the assault, whether heeded or not by an Israeli government with a historically uneasy relationship with President Obama.

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Already, Palestinian health officials say, 194 people in Gaza have been killed and 1,400 wounded in the Israeli assault, designed to suppress Hamas rocket fire into a widening perimeter of Israeli towns and cities. The Gaza death toll has surpassed the level of 2012, when Israel and Hamas last exchanged intensive fire. That conflict ended after eight days, with a direct diplomatic intervention by Washington.

This time, the administration has been careful not to criticize Israel or publicly suggest a deadline to end the military action.

“We don’t have somebody on the other side who’s willing to stop firing,” Ron Dermer, the country’s ambassador to Washington, said in an interview.

In rejecting the truce offer, Hamas said it had never been consulted on the terms, which it considered unacceptable. The rejection, though, was a sign of the group’s independence from traditional Arab power brokers, particularly Egypt, whose new secular government has virtually no influence over the Islamist organization.

It is not clear whether any country or group holds enough influence with the militants to effect a truce, as politics and alliances across the Middle East are shuffled by civil war and popular protest.

“I don’t know what will happen if Hamas decides in 10 minutes or an hour or in a day to actually completely cease fire,” Dermer said. In the meantime, “we have to take the action in order to defend ourselves.”

Israel says its bombing campaign is defensive and not aimed at displacing the Hamas leadership in Gaza or eliminating its stockpiles of weapons.

View Graphic The Iron Dome defense

U.S. officials said Tuesday that the goal should still be a cease-fire, but they did not set any terms.

“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,” Secretary of State John F. Kerry said before the truce fell apart.

Palestinian officials urged other countries to press Israel to stop the campaign and end its economic blockade of Gaza.

“You can’t lay siege to people and then start bombing them and attacking them,” said Hanan Ashrawi, a member of the Palestine Liberation Organization’s executive committee.

Hamas leaders have shown no inclination to pull back daily rocket attacks launched toward Israeli cities. The militant group has little incentive to negotiate now, and may fear that talks with Israel could weaken its hold on Gaza. The movement seized full control of the small territory in 2007, two years after Israel withdrew occupying forces.

White House press secretary Josh Earnest placed the onus on Hamas and other armed groups to accept Egypt’s offer and stop cross-border attacks.

“All eyes now turn to Hamas and the groups in Palestinian-held territories who are firing rockets,” he said. “The question for them is whether or not they are going to abide by the cease-fire agreement that was put forward by the Egyptians.”

But, Earnest noted, “what we would ask the Israelis to do is to exhibit some concern for the safety and welfare of innocent civilians who are at risk of being caught in the crossfire.”

Cairo’s new military-backed government has renounced a close relationship with Hamas and cooperated with Israel to seal off tunnels that supply weapons, food and goods to Gaza. The effect is to support Israel’s blockade of the militant-governed Palestinian Arab territory, although Egypt is officially cool to the Jewish state.

Egypt’s offer did not meet well-known Hamas demands, including the reopening of a key border crossing. But U.S. officials called the offer a “live option” that could be the basis for a longer-term agreement to stop rocket attacks.

Kerry repeated a U.S. offer to help end the cross-border attacks and foster negotiations, although Israel has shown no sign that it wants that direct intervention.

Kerry scrapped tentative plans to travel to Arab states that might hold influence with the Hamas militants this week, opting to return to Washington after several days of negotiations in Vienna over Iran’s nuclear program.

Qatar, which funds several Islamist militant groups, may be best placed to pressure Hamas to scale back rocket attacks and accept a cease-fire. But Qatari officials have said little about the conflict, and left the diplomatic gesture to Egypt.

Former Egyptian president Mohamed Morsi helped broker a cease-fire in 2012, alongside hurried shuttle diplomacy by then-Secretary of State Hillary Rodham Clinton. Then, Clinton urged Israel to curtail its offensive and the Muslim Brotherhood-backed Morsi used his Islamist credentials and connections to Hamas to rein in the militants.

Morsi was deposed in a military coup last year, and Egypt immediately began cutting ties to Hamas and Gaza, which borders Egypt. Iran also has withdrawn much of its longtime support and weapons help for Hamas, and former protectors in Syria are consumed with fighting a civil war.

Kerry has not been invited to Israel for a replay of the 2012 shuttle mission, although State Department spokeswoman Jen Psaki said Tuesday that he would be willing to try.