As they vow to deal a decisive blow to the military capability of the militant Lebanon-based group Hizbullah, top Israeli officials have outlined goals ranging from degrading Hizbullah's military capability to crushing the organization completely.
The top priority, Israeli officials say, is to secure Israel's northern border with Lebanon without reoccupying land inside southern Lebanon.
But how they plan to achieve that is less clear.
"Israel's strategy is probably a dynamic one, which means it is reinventing itself according to developments in the field," says Shaul Mishal, a professor at Tel Aviv University. "I'm not sure the political establishment was aware when this military operation began that it was going to lead to such an intensive military campaign and fire exchange."
With militant groups in the region backed mainly by Iran and Syria, defining victory against such asymmetric threats has been a problem for Israel since the last regular war it fought in 1972 against Egypt and Syria.
The central question, says Dan Schueftan, deputy director of the National Security Studies Center at the University of Haifa, is: "At the end of a certain confrontation, is Israel's position better and is the enemy's worse?"
Sunday, eight Israelis were killed and dozens wounded when a Katyusha rocket struck a train depot in Haifa, raising tensions in the northern city, which was also hit Thursday by rockets for the first time in 15 years. Hours later, Israel responded with at least six air strikes on southern Beirut, targeting Hizbullah headquarters.
Israeli authorities put residents across the north and in the central city of Tel Aviv on heightened alert in an acknowledgment of the longer-range missile attacks.
Lebanon's Prime Minister Fouad Siniora asked Sunday for UN help to promote a cease-fire. He said that he wanted his government to exert control over southern Lebanon, where Hizbullah is entrenched. Also Sunday, European Union foreign policy chief Javier Solana arrived in Beirut Sunday for talks. Lebanon also said that Italy's Prime Minister Romano Prodi had relayed Israeli conditions for a cease-fire.
"Prodi told me that Israeli Prime Minister Ehud Olmert informed him of two demands for a cease-fire – handing over the two captive Israeli soldiers and a Hizbullah pullback to behind the Litani River," a government statement quoted Siniora as telling the cabinet.
Most analysts here says that the strong support for Hizbullah from Lebanon's 40 percent Shiite population makes total destruction of the group impossible. Mindful of repercussions, Israel says it is trying to avoid causing irreparable damage to Lebanon.
"We didn't remove the gloves completely," a high ranking military official told reporters over the weekend. "We need to be very careful that we only put enough pressure on the Lebanese government to change the situation but not enough to make it fall."
But with Sunday's attack on Haifa bringing the death toll here to more than 20 in the past five days, both the government and the population – which strongly backs the campaign – may not be satisfied with simply striking back.
Writing in the Hebrew newspaper Haaretz, Israeli commentator Aluf Benn said the government is also making a strong show of force in order to deliver the message that attacks into Israeli land not under dispute will be dealt with on a different scale than those staged inside occupied territory.
"[Olmert] wants to set a precedent for the convergence plan in the West Bank [under which Israel would make further unilateral land withdrawals] and to show that Israel won't accept terror from beyond the fence after it withdraws, as it got from Lebanon and from Gaza," he wrote.
But whereas Israel could unilaterally and relatively easily degrade Hizbullah military might, creating a new paradigm in the north may prove difficult on multiple fronts, says Gidi Grinstein, the President of the Reut think tank in Tel Aviv, who headed the Israeli negotiating team at the 2000 Camp David Summit.
"It would require pushing back Hizbullah from the border, and either an international force or the Lebanese army taking control of the south – and that's not entirely under our control," Mr. Grinstein says.
Though a spokesman from Israel's Foreign Ministry says the government "understands the solution is not military but political," Israeli officials have yet to engage in diplomacy, at least publicly.
The combination of military pressure and diplomacy is probably the only way to avoid a full-blown regional war on one hand, or what would be perceived as capitulation by Israel. "That's what you do in the Middle East," says Professor Mishal. "While you beat each other, you kiss each other too, even if it's under the table."
But the game of brinkmanship now under way between Israel and Hizbullah is a dangerous one no matter what the ultimate goal is, says Yoram Meital, a Middle East expert at Ben-Gurion University. The situation "can spiral into something much more complicated and dangerous than what it is now, both in Gaza and Lebanon," he says.
• Orly Halpern contributed reporting to this story. Wire material was also used.