Early in the current clash between Hamas and Israel, much of the drama was in the air. The Palestinian terrorist group launched hundreds of rockets at Israel, and Israel responded by knocking down rockets in the sky with its Iron Dome defense system and by bombing the rocket-launch sites in Gaza. But the real story has been underground. Hamas’s tunnels into Israel are potentially much more dangerous than its random rocket barrages.

Israel started a ground offensive against Hamas in Gaza on Thursday, intending to destroy Hamas’s tunnel network. The challenge became obvious on Saturday when eight Palestinian fighters wearing Israeli military uniforms emerged from a tunnel 300 yards inside Israel and killed two Israeli soldiers in a firefight. One of the Palestinian fighters was killed before the others fled through the tunnel back to Gaza.

According to Yigal Carmon, who heads the Middle East Media Research Institute, his organization’s monitoring of published material and discussions with Israeli officials indicate that Hamas’s tunnels—and not the well-publicized episode of kidnapping and murder involving young Israelis and a Palestinian teenager—were the spark for the conflict.

Consider: On July 5 Israeli planes damaged a tunnel dug by Hamas that ran for several kilometers from inside the Gaza Strip. The tunnel emerged near an Israeli kibbutz named Kerem Shalom —vineyard of peace.

That Israeli strike presented Hamas with a dilemma, because the tunnel was one of scores that the group had dug at great cost. Were the Israelis specifically aware of the tunnel or had their strike been a random guess? Several members of the Hamas military leadership came to inspect the damage the following day, July 6. A later official Israeli report said that the Hamas inspectors were killed in a “work accident.” But what if the Israelis had been waiting for the follow-up and struck again?

Hamas now saw its strategic plan unraveling. The tunnel network gave it the ability to launch a coordinated attack within Israel like the 2008 Islamist rampage in Mumbai that killed 164 people. Recall that in 2011 Israel released more than 1,000 Palestinian prisoners, more than 200 of whom were under a life sentence for planning and perpetrating terror attacks. They were exchanged for one Israeli soldier, Gilad Shalit, who had been taken hostage in a cross-border raid by Hamas. Imagine the leverage that Hamas could have achieved by sneaking fighters through the tunnels and taking hostages throughout Israel; the terrorists intercepted Saturday night were carrying tranquilizers and handcuffs.

If the Israeli strike on the tunnel near the Kerem Shalom kibbutz presaged a drive to destroy the entire network—the jewel of Hamas’s war-planning—the terrorist group must have been thrown into a panic. Because by this summer Hamas was already in desperate political straits.

For years Hamas was receiving weapons and funding from Shiite Iran and Syria, under the banner of militant resistance to Israel. But when Mohammed Morsi became president of Egypt in June 2012, Hamas abandoned its relationship with Iran and Syria and took up instead with Mr. Morsi and the Sunni Muslim Brotherhood. Hamas also took up with Turkey and Qatar, also Sunni states, describing them at one point as the saviors of Hamas. Former benefactors Syria and Iran then called Hamas traitorous for abandoning the resistance-to-Israel camp.

The Hamas romance with Mr. Morsi was especially galling to Shiite-led Iran and Syria. The Shiites are only 10% of the world’s Muslims, and neither Iran nor Syria welcomed the loss of a patron to Sunni Egypt. The coup that removed Mr. Morsi and the Muslim Brotherhood regime in June 2013 brought a chill in Egypt’s relationship with Hamas that has kept Egypt’s border with Gaza closed, denying Hamas that route of supply.

But Iran and Syria did not rush to embrace their former beneficiary. When Hamas tried to re-ingratiate itself with Iran this May, its political bureau head, Khaled Mash’al, was denied an audience in Tehran and could only meet a minor diplomat in Qatar. On June 26 the Iranian website Tabnak posted an article titled, “Mr. Mash’al, Answer the Following Questions Before Asking for Help.” The questions included: “How can Iran go back to trusting an organization that turned its back on the Syrian regime after it sat in Damascus for years and received all kinds of assistance?” and “How can we trust an organization that enjoyed Iranian support for years and then described Turkey and Qatar as its saviors?”

So on July 6, Hamas stood politically isolated and strategically vulnerable. It had lost the financial support of Egypt and could not get renewed support from Iran in the measure it needed. To some in the organization it appeared that Hamas had only one card to play—and on July 7 it played that card with rockets. As to the tunnels, last Thursday Israeli forces intercepted 13 armed terrorists as they emerged from a tunnel near Kibbutz Sufa in Israel.

There are other messages out there for the Palestinians instead of the violent one sent by Hamas. Writing in the London-based Arabic daily Al Hayat on July 12, Saudi intellectual Abdallah Hamid al-Din, no friend of Israel, urged Palestinians to abandon as unrealistic demands for a right of return, and to forgo as hypocritical calls to boycott Israel:

“The only way to stop Israel is peace. . . . Israel does not want peace, because it does not need it. But the Palestinians do. Therefore it is necessary to persist with efforts to impose peace. No other option exists. True resistance is resistance to illusions and false hopes, and no longer leaning on the past in building the future. Real resistance is to silently endure the handshake of your enemy so as to enable your people to learn and to live.”

Plenty of others are sending the same message today. Whether Palestinians will listen is another matter.

Mr. Mukasey served as U.S. attorney general (2007-09) and as a U.S. district judge for the Southern District of New York (1988-2006).