THE DISTINGUISHING feature of the latest war between Israel and Hamas is “offensive tunnels,” as the Israeli army calls them. As of early Wednesday, 28 had been uncovered in Gaza, and nearly half extend into Israel, according to Israeli officials. The tunnels are the reason that the government of Benjamin Netanyahu decided last weekend to launch a ground invasion of Gaza, and they explain why that operation has strong support from Israelis in spite of the relatively heavy casualties it has inflicted. Most significantly, the tunnels show why it has been difficult to reach a cease-fire and why any accord must forge a new political and security order in Gaza.

Hamas’s offensive tunnels should not be confused with the burrows it has dug under Gaza’s border with Egypt to smuggle money, consumer goods and military equipment. The newly discovered structures have only one conceivable purpose: to launch attacks inside Israel. Three times in recent days, Hamas fighters emerged from the tunnels in the vicinity of Israeli civilian communities, which they clearly aimed to attack. The ­concrete-lined structures are stocked with materials, such as handcuffs and tranquilizers, that could be used on hostages. Other tunnels in northern Gaza are designed for the storage and firing of missiles at Israeli cities.

The resources devoted by Hamas to this project are staggering, particularly in view of Gaza’s extreme poverty. By one Israeli account, the typical tunnel cost $1 million to build over the course of several years, using tons of concrete desperately needed for civilian housing. By design, many of the tunnels have entrances in the heavily populated Shijaiyah district, where the Israeli offensive has been concentrated. One was found underneath al-Wafa hospital, where Hamas also located a command post and stored weapons, according to Israeli officials.

The depravity of Hamas’s strategy seems lost on much of the outside world, which — following the terrorists’ script — blames Israel for the civilian casualties it inflicts while attempting to destroy the tunnels. While children die in strikes against the military infrastructure that Hamas’s leaders deliberately placed in and among homes, those leaders remain safe in their own tunnels. There they continue to reject cease-fire proposals, instead outlining a long list of unacceptable demands.

One of those demands is for a full reopening of Gaza’s land and sea borders. While this would allow relief and economic development for the territory’s population, it would also allow Hamas to import more missiles and concrete for new tunnels. Secretary of State John F. Kerry, the Egyptian government and other would-be brokers are right to seek a cease-fire, but they should reject Hamas’s agenda. Instead, any political accord should come after a cease-fire and be negotiated with the Palestinian leadership of Mahmoud Abbas. It should link opening of the borders and other economic concessions to the return to Gaza of the security forces of the Palestinian Authority, the disarmament of Hamas and elections for a new government.

In setting such conditions, international mediators will likely have the quiet support of most of Gaza’s population. Polls show that they are fed up with Hamas’s rule and with its use of women and children as cannon fodder in unwinnable wars with Israel. The next government of Gaza should be one that invests in schools, health clinics and houses, not in tunnels.