Israel is in some ways two countries these days. The border between them runs eastward from the southern outskirts of Haifa on the Mediterranean to the Sea of Galilee. Above this line, the rockets and missiles are falling. Much of the population has left, and a good part of those who haven’t spend their days in or within running distance of shelters. Commercial life has been paralyzed. Stores are closed, businesses shut down.

Below the line, all is different. My wife and I live in a town just to the south of it, half-an-hour’s drive from Haifa. We’ve had a few air-raid sirens and have now and then heard the whump-whump-whump of incoming fire falling far away, but that’s about it. The shops and cafés are crowded and the streets are full of people, not a few of them refugees from the north staying with relatives or friends. You wouldn’t know from looking at them that there was a war going on.

There are other things, too, that can make the fighting in Lebanon seem far away for those living in the country’s center and south, which felt no less threatened than the north by Saddam Hussein’s Scuds in the 1991 Gulf War. Relatively few reserve soldiers have been called up, and a much smaller percentage of the population does reserve duty than was once the case, so that few families have had fathers or sons taken suddenly away and placed in danger. Nor are there the nightly blackouts that Israelis remember from the 1967 and 1973 wars. Rockets and missiles fly blind by night and day.

And yet nevertheless, as the weeks of fighting have lengthened, Israelis everywhere have grown more and more aware that their country is fighting a real war. What started out as an apparent border skirmish, and then quickly became a wider conflict, is now, the country has increasingly begun to feel, a fight for Israel’s existence.

Not, of course, for its immediate physical existence. Although the material damage wreaked by Hezbollah on Israel’s northern towns and cities has steadily accumulated, it is still, relatively speaking, not great.The country will recover from it quickly.

What has begun to penetrate, rather, is that this is a war that Israel cannot afford not to win. Any end to it that leaves Israel’s Arab and Islamic enemies with the impression that Israel has been beaten, or even fought to a draw, will seriously endanger its future.

To a great extent, after all, Israel went to war a month ago, after the abduction of three of its soldiers and the killing of several others, to reassert its deterrent power in the face of a radical, Iranian-backed Islamic organization that had, in the six years since the Israeli withdrawal from southern Lebanon in 2000, taken over the area, fortified itself in military bastions, and armed itself to the teeth while Israel looked on and did nothing. And throughout those six years, drunk on the conviction that it had expelled Israel from the Lebanese south by force of arms, this organization told the Arab and Muslim worlds that Israel was a “cobweb” that could be easily brushed away. Show the resolution and fighting spirit that we did, Hezbollah’s message went, and the Zionist state can be destroyed.

This is not a message to be taken lightly, especially not when its main audience is the Palestinian people, the people and government of Iran, and Islamic jihadism everywhere. A Zionist state that can be destroyed is a Zionist state that it is worth actively planning to destroy.

Clearly, in going to war Israel erred in thinking Hezbollah too much of a cobweb itself. Hezbollah has fought well, cleverly, and resiliently, and has turned out to have had far more extensive bunkers and concealed positions than it was thought to have. These are Israeli intelligence blunders for which there is little excuse when one considers the fact that the Israeli army already saw in the mid-1990s that Hezbollah fighters were a new breed of Arab soldiers and that southern Lebanon was an area in which Israel had extensive contacts and should have had effective agents.

But this is now beside the point, as is the question of whether Israel could have gotten just as good or better results had it acquiesced in calls for a ceasefire three weeks ago, when the Lebanese government and part of the Arab world might have supported a document like the current U.S.-French draft resolution — which would administer a resounding defeat to Hezbollah if implemented — that they are now opposed to. These are now subjects for historians, not for Israel’s government and army chiefs.

What matters to Israel now is to make this resolution implementable. And without the Lebanese government and moderate Arab states behind it, the only way to do so is to go on fighting, inch by inch if necessary, until Hezbollah has been driven out of all of the territory that the multi-national buffer force envisaged by America and Europe is expected to occupy. No one, not this force and not the Lebanese army, is going to do this on Israel’s behalf — and unless Israel can take this territory and sit firm in it until the government of Lebanon agrees to accept the American-French draft, Hezbollah will remain in, and return to, the Lebanese south and Israel will have failed to win the war.

To achieve a diplomatic victory, Israel first has to win a military victory. This does not have to be total. If Hezbollah survives outside of the Lebanese south, Israel can live with this. But if it doesn’t prosecute the war until Hezbollah is gone from the south it will give aid and comfort to those who are already planning the next war against it. There are few Israelis who do not by now realize this.

Mr. Halkin is a contributing editor of The New York Sun.