On Saturday, Israel and Hamas observed a 12-hour cease-fire, creating a brief respite in fighting in the Gaza Strip. Israel later announced that it had agreed to a four-hour extension of the pause.

In other conflicts, cease-fires are usually considered an informal agreement to stop fighting, often with the aim of figuring out a formal accord on a return to peace-time relations. This cease-fire isn't quite like that. It's a "humanitarian cease-fire," designed to give those living in Gaza's hardest hit areas some relative peace and allow ambulances to visit those areas. Once the cease-fire ends, fighting will presumably resume. The world's diplomatic elite, including Secretary of State John F. Kerry, are hoping that a broader truce can be struck. Kerry himself put forward a plan for such a cease-fire on Friday, but it was rejected by Israel.

To understand why Kerry's cease-fire plan failed, it helps to understand what a "cease-fire" really means in the reality of the current Israel-Palestinian conflict. While its not exactly a war, the conflict has been escalating and de-escalating for years, occasionally flaring up into full warfare at points. In this context, Kerry's cease-fire doesn't really look like a chance for a return to peace: It looks like a break from fighting and a return to a lower, yet still uncomfortable, level of hostilities that will probably soon flare up again. Israel has targeted Gaza, with the hope of crushing Hamas, four times since the Palestinian Islamist group came to power in 2007. Even if a cease-fire is agreed on soon, a betting man might predict the two sides will be trying to reach another one in a couple of years.

That's a big problem. Numerous public opinion polls have shown that for all the international criticism of Israel's offensive in Gaza, it remains popular within Israel. Jodi Rudoren, the New York Times' Jerusalem bureau chief, helped to explain this earlier this week, when she noted that many Israeli's didn't want to leave a job "half-finished," with Gaza the same "launching pad for rockets" that it has been since Israel withdrew in 2005. Also, in a new twist, Israel is now dealing with underground tunnels that go directly into Israel and that Hamas hopes to use for attacks. Prime Minister Benjamin Netanyahu had actually risked public opinion by agreeing to an earlier, Egypt-brokered cease-fire (Hamas, which says it wasn't directly consulted, wouldn't agree to it), but the rejection of Kerry's plan suggests he may not risk it again. "Israel must be permitted to crush Hamas," is how Michael Oren, Israel’s ambassador to the United States from 2009 to 2013, put it in an op-ed for The Post published Thursday. Reports that Israel hopes to expand its ground operation suggest that may be the way things are heading.

Amid renewed fighting between Israel and the Palestinian territories, The Post’s Ishaan Tharoor offers a background on the decades-old conflict and the current escalation. (Davin Coburn/The Washington Post)

For Hamas, too, a return to the conflict's recent status quo is exactly what it doesn't want. Hamas has repeatedly made clear that it is seeking an end to the eight-year Israeli blockade on Gaza, and it doesn't appear to be willing to negotiate on that. Many residents in Gaza appear to support that. “We want a good life or no life,” Ibrahim Zain, a Gaza resident who is unemployed, told the Associated Press this week. In particular, Hamas doesn't want a cease-fire that would vaguely agree to talks about opening the borders: It wants a cease-fire that definitely allow the borders to be open before it and other militant groups stop shooting missiles. Israel doesn't want to open the borders until the missiles can definitely be stopped. Given that Hamas rejects Israel's right to exist and refuses to renounce violence, that's not totally unreasonable.

Kerry recognizes this. “I understand that Israel can’t have a cease-fire in which . . . somehow the tunnels are never going to be dealt with. The tunnels have to be dealt with," he said Saturday.“By the same token, the Palestinians can’t have a cease-fire in which they think the status quo is going to stay."

Of course, what gets lost in all this focus on a cease-fire is the longer-term issues for Israelis and Palestinians -- potential Palestinian state borders, the status of Jerusalem, issues with refugees, Israeli settlers and much more. And, as my colleague Ishaan Tharoor notes, one of the big hopes for a lasting peace between Israel and Palestinians, the two-state solution, looks increasingly distant. If a short-term cease-fire is so hard to achieve, what hope is there for anything longer-term?