The Obama White House and others, inside and outside governments, have talked about a “limited” strike against Syria. They have cited a need to punish the regime of Bashir al-Assad for conducting a deadly chemical weapons attack last week in the Damascus suburbs. The military response, likely a wave of cruise missiles, would be designed as a deterrent against future use of the outlawed weapons, putting Assad on notice that further attacks would bring additional wreckage.

There is much logic in John Kerry, the secretary of state, declaring: “President Obama believes there must be accountability for those who would use the world’s most heinous weapons against the world’s most vulnerable people.” Yet such a strike isn’t something for which the ground has been prepared, diplomatically and politically.

Many in the United States, France, Britain and elsewhere may be persuaded about the fact of a chemical attack — in the accounts of local doctors, intercepted phone calls and disturbing video. What would make the case is a corroborating report from U.N. weapons inspectors, now on the scene in Syria, the findings setting the stage for discussion and action at the United Nations. On Wednesday, Britain called for introducing a resolution at the Security Council accusing Syria.

Essential to gaining the necessary moral authority, yes, even against a regime as loathsome as the one led by Assad, is making a powerful, evidence-packed argument. That may not bring along Russia. It would make plain to the assembled nations the line that Assad has crossed.

Yet, in an important way, the effort shouldn’t be limited. That doesn’t mean becoming more involved in the fighting of a civil war now in its third year. The White House missed long ago the opportune moment for supporting the rebels. Rather, as Zbigniew Brzezinski argued in the Financial Times this week, this discussion of chemical weapons serves as an invitation to the president to engage in a global effort at containing, even resolving eventually, the destructive conflict in Syria.

The veteran foreign policy strategist emphasized the stakes, an escalating war spilling more deeply into Jordan and the rest of the region, sending tremors into Iraq and Lebanon, disrupting Palestinians and Israelis, Turks and Kurds, perhaps stretching to the Caucasus region of Russia. Asian countries rely heavily on Middle East oil. Surely, China, Japan and India should be wary.

The suggestion isn’t that this would be anything but hard. The point is, the Syrian use of chemical weapons should lead to something more than “limited” punishment. It should trigger urgency, in a full political and diplomatic response.