This is seen as another step in preparation for a major ground confrontation.
The goal of Operation Protective Edge is to reduce to zero the attacks from Gaza, Israel says. Hamas will pay a heavy price, as it has already begun paying, in order for it to understand Israeli citizens are not to be fired at, the administration says.
Israel says it has a duty to provide security to its citizens and continuing the attacks on Hamas is the right way to provide the security. In the meantime, more than 90 Palestinians, including more than 20 children, are the latest victims.
An extended campaign against militants in Gaza seems more likely with every passing day. Both sides resorted to a show of military strength after a series of quick-fire events illustrated the extreme fragility of Israeli-Palestinian relations, starting with the collapse of American-sponsored peace talks, attempts by rival Palestinian factions to form a coalition government, the kidnapping and killing of three Israeli teenagers and the subsequent kidnapping and murder of a Palestinian teenager.
Israel Prime Minister Benjamin Netanyahu's Government is under pressure to restore quiet to southern Israel, where many thousands of Israelis fled to shelters and schools were shut. The Government is also under pressure for a more extensive operation, including ground troops, to destroy a military infrastructure in Gaza rebuilt since Israel's last campaign there in 2012.
At the same time, Hamas needs to show more radical groups in Gaza it can stand up to Israel. Weakened by the installation of an antagonistic military-backed Government in Egypt that has moved to seal the border with Gaza, sharply reducing Hamas' tax receipts, and having little to show for its coalition with Fatah, Hamas appears to have fallen back on its main principle of armed resistance to Israel.
Hamas will find it difficult to walk away from this round of conflict without something to persuade its own people the death and destruction in Gaza has achieved something. It will want prisoners released as part of the deal. Israel will be reluctant.
The pressure on public opinion also weighs on Israel, which has talked in terms of a final end to the rocket threat from Gaza. This is regarded as a tall order when Israel itself estimates Hamas has a stockpile of 10,000.
There have been plenty of diplomatic reputations destroyed trying to negotiate peace in the Middle East, particularly on the vexed issue of Israel's relationships with its neighbours. Israel aggressively protects its boundaries, whether or not the world sees the country as being in the right or the wrong.
The leaders of France and Germany have condemned the attacks on Israel. United States Secretary of State John Kerry has spoken with Mr Netanyahu and plans to speak with Palestinian Authority President Mahmoud Abbas. US officials have been encouraging all sides to de-escalate the situation, the US State Department says.
The situation can be compared with the one playing out in the Ukraine, where after the annexation of Crimea, Russia faced trade and financial blockades. As Russia pushed its case further, sanctions were tightened, overseas accounts frozen and trade deals delayed.
Nothing is appearing on the horizon to suggest Israel and Hamas will end their current dispute any time soon. Mr Netanyahu says the situation is one of escalation rather than de-escalation. Hamas has warned it will continue to retaliate and called on Palestinians to unite.
It may seem too simplistic and obvious, but the threat of withdrawing financial support from both Hamas and Israel may have the desired effects of calming down the situation. Both regimes are spending millions on hundreds of attacks on military and civilian targets. Without trade and money, a rethink may be possible. The United Nations is now involved - not before time. Until even a partial solution is reached, many more people will be tragically and needlessly killed.
