Last Tuesday, Israel faced the fallout from a Palestinian family of five perishing in the Gaza Strip during an Israeli strike against militants firing rockets at an Israeli town. On Wednesday, the Bush administration woke to a front-page picture in The Post of a 2-year-old Iraqi boy killed in a U.S. airstrike in Baghdad aimed at Shiite militiamen launching rockets at the city's Green Zone. The similarity of these tragic and politically costly episodes was anything but a coincidence.

For months now, Israel has been mired in an unwinnable war against Hamas and allied militias in Gaza, who fire missiles at civilians in Israel and then hide among their own women and children, ensuring that retaliatory fire will produce innocent victims for the Middle East's innumerable satellite television networks. A growing number of the militiamen have been to Iran for training, and some of the missiles they launch are Iranian-made. Their objective is obvious: to exhaust Israelis with an endless war of attrition while making it impossible for Israel's government to reach a political settlement with the more moderate Palestinian administration in the West Bank.

Now U.S. forces have been drawn into a similar morass in Sadr City, the Shiite neighborhood of 2 million ruled by Moqtada al-Sadr's Mahdi Army. As Iranian-made rockets rain down on the Green Zone and nearby neighborhoods, U.S. forces attempt, so far in vain, to stop the fire by attacking Shiite militants from the ground and the air. Hundreds of people have been killed, filling the satellite airwaves and handing a new argument to the "this war is lost" lobby in Washington.

It's not hard to grasp the common strategy at work here or to intuit what interest it serves. The rockets fired from Gaza and from Sadr City are two prongs of an offensive aimed at forcing the United States out of Iraq, putting Israel on the defensive -- and leaving Iran as the region's preeminent power. The third front, in Lebanon, is also the model. There the Hezbollah militia has armed itself with thousands of rockets and long-range missiles in preparation for a repeat of its 2006 war with Israel, while making Tehran a power in domestic Lebanese politics. The fourth front is in Afghanistan, where Taliban militiamen near the Iranian border now come armed with Iranian-made weapons.

Countering the strategic Iranian challenge -- which also includes its unimpeded nuclear program -- is likely to preoccupy U.S. policy in the Middle East for years. But the more immediate problem for both the United States and Israel is how to end the wars of the rockets. As Israel has demonstrated over the past 18 months, selective strikes against rocket crews by aircraft or special forces can inflict a lot of casualties -- but don't stop the launchings. As U.S. forces have shown in Baghdad, sending substantial ground forces into Sadr City (or Gaza), building walls and fighting for control of the streets doesn't bring quick relief, either. Israel has so far avoided a similar offensive in Gaza in part because of another problem, the lack of an exit strategy. Even if the streets can be cleared of militants, who will ensure that no rockets are fired after the invading forces depart? Neither Iraqi nor Palestinian government forces seem up to the job.

Both Israelis and Americans are tantalized by the prospect of a political solution. With U.S. encouragement, the Iraqi government is negotiating with both Sadr and Iran; Israel is talking to Hamas through Egypt. Both militias say they would be happy to observe a cease-fire in exchange for political concessions. (Sadr has already announced one, though the rocket launches continue.) But neither will agree to disarm. This is again the model of Hezbollah, which participates in the Lebanese parliament but refuses to give up its weapons, giving it the ability to wage war at any time of its -- or Tehran's -- choosing. Hamas will not surrender its option to bleed Israel, nor will the Mahdi Army its means to harry the American enemy.

Some think all this can be settled by a direct approach to Tehran by the United States and a grand bargain that would stop the flow of weapons and trainers to Baghdad, Gaza, Lebanon and Afghanistan, along with the nuclear weapons program. In exchange for what? Never mind: The next president, especially if a Democrat, will probably try it. But let's hope Barack Obama, Hillary Clinton and John McCain also are thinking about a grimmer possibility: that Iran believes that its offensive is succeeding and that its goals are within reach, and that it has no intention of stopping. As long as neither Israeli nor U.S. commanders can find a way to win the war of the rockets, that's likely to be the case.