For the past three weeks, the world has been focused upon Israel’s northern border where the intense confrontation with Hezbollah rages. The Hamas attack across the Gaza border and capture of an Israeli corporal seems like ancient history. And while Hamas fighters in Gaza may have first welcomed the violent gesture of solidarity from their ideological brethren in the north, they have lost a lot as a result. The northern conflict drained any sympathy Hamas had gained for being the elected leadership of the oft-pitied Palestinians as the world re-learned the reality that, like Hezbollah, Hamas is a terrorist proxy of Syria and Iran.

With Secretary of State Rice and other international diplomats stepping up their pace to fashion a ceasefire package for U.N. Security Council ratification this week, it is critical to remember that Hamas was launching rockets at civilian targets inside Israel from Gaza in the south long before Hezbollah opened the northern front.

Hezbollah is properly seen as the aggressor against Israel in violation of international law.The “blue line” border between Israel and Lebanon that Hezbollah crossed to kill and abduct Israeli soldiers and has since been launching rockets over was formally recognized by U.N. Security Council Resolution 1559, which also recognized that, after several years of occupation, Israel had fully withdrawn from Lebanon.

Moreover, even in the face of the tragic collateral damage to the Lebanese, there is also recognition that Hezbollah is in violation of international law when it positions its rockets and personnel in the midst of civilian neighborhoods and that Israel is not responsible, as a matter of international law, when it targets such strongholds as part of its defensive action.

Even as some qualify their position with humanitarian concerns and statements about the proportionality of Israel’s tactics, responsible international leaders have recognized that in responding to Hezbollah’s attacks, Israel is acting in its own self defense in a manner consistent with international law as codified in Article 51 of the U.N. Charter.

All of the above stands in stark contrast to Israel’s southern battleground, where it confronts Hamas. Over the past year — after Israel fully withdrew its citizens and soldiers from Gaza — Hamas launched as many rockets into Israeli civilian areas as Hezbollah launched in a recent fortnight. As Hezbollah did in the most recent provocation in the north, Hamas crossed into Israel and abducted an Israeli soldier. And like Hezbollah, Hamas is directly tied to Syria — with Hamas leader Khaled Mashal based in Damascus — and receives funding and weapons from Iran.

What Israel has been sorely lacking in its confrontation with Hamas is any international recognition of its full withdrawal from Gaza. Irrespective of Cpl. Shalit’s return, a final Security Council resolution on the conflict must not only set the parameters of an international monitoring force, hold Syria and Iran accountable for Hezbollah’s actions and more, it must include the explicit recognition that Israel withdrew from Gaza and that attacks by Hamas across the Green Line in the south are as illegitimate as anything Hezbollah perpetrated in the north. Hamas may not position rockets among Gaza’s civilians, nor launch them into Israel; and if they do, Israel is within its international legal rights to retaliate.

Just as Hezbollah’s participation in the government of Lebanon did not absolve them of the international culpability for being the aggressor in the current conflict, so too Hamas’s role in the Palestinian Authority must not exculpate their terrorist acts.

The inclusion of these provisions regarding the southern front should be appealing across the political spectrum. Those who wish to see Israel make further withdrawals from West Bank territory must give Israelis some hope that doing so would afford them greater protection from any cross-border assaults, and providing such assurance on the Gaza front now is critical in doing so. Those who wish to see Israel empowered to deter Iran’s proxies and retaliate against them when necessary must arm Israel with the legitimacy of international law.

Armed conflicts can inspire confusion or clarity in foreign affairs. So far, the conflict in Israel’s north has clarified the world’s thinking with regard to the threat from Iran, terrorist proxies and more. Such clarity must not be lost among leaders as they turn their gaze to Israel’s south, for to do so sows the seeds of confusion and ensures further conflict.

Mr. Diament is director of public policy of the Union of Orthodox Jewish Congregations of America.