FOLLOWING THE failure of their diplomatic effort to persuade Russia not to seize Crimea, the United States and its allies must fashion a new policy toward the regime of Vladi­mir Putin: a long-term effort to counter and eventually reverse his aggression.

After an orchestrated “referendum” on Sunday, Mr. Putin may leave the region — and Ukraine — in limbo for an extended time. Alternatively, he might move swiftly to annex the territory, breaking one of postwar Europe’s strongest taboos. He could even carry out the invasion of eastern Ukraine threatened by Russian troop maneuvers; on Saturday, Russian troops were reported to have seized a Ukrainian gas-pumping station and village outside Crimea.

Whatever his course, the United States and the European Union should quickly and forcefully bolster the Ukrainian government and assist it in carrying out economic reforms and democratic elections. But the West must also embrace the goals of punishing and, over time, weakening Mr. Putin’s regime.

The Obama administration and the European Union are poised to adopt sanctions as early as Monday against Russians involved in the invasion, denying them visas and freezing their assets. But it’s not clear that those measures will be aimed where they must be: at the relatively small circle of oligarchs and power brokers who surround Mr. Putin. These include Igor Sechin, chairman of the oil company Rosneft; Vladi­mir Yakunin, president of Russian Railways; and Alexei Miller, chairman of Gazprom. Russia is ruled by a mafia. If the dons are left untouched, Western sanctions will have little effect.

Western strategy must also fulfill the warning issued by German Chancellor Angela Merkel, who said the invasion would “cause massive damage to Russia, economically and politically.” That means, at a minimum, excluding Moscow from the Group of Eight and the Organization for Economic Cooperation and Development, which it is seeking to join. It also requires expanding sanctions from individuals to sectors — starting with the Russian banking system, which should be cut off from U.S. and European markets. Russia will respond with sanctions of its own, including against Western companies in Russia. Governments must be prepared to discount that damage, knowing that the economic cost to Russia — including from its own sanctions — will be far greater.

The most important piece of the Western response will be staying power. The policy probably won’t bring quick results, other than Russian retaliation. Mr. Putin may respond with more aggression. He may seek an early “normalization” of relations, dangling as a lure Moscow’s supposed influence over Iran and Syria or its facilitation of shipping to Afghanistan. The Obama administration should not abandon its work with Russia in these areas, but it also cannot temper its reaction to the situation in Crimea on behalf of other interests. If Mr. Putin threatens to suspend cooperation, the response should be to call his bluff.

Mr. Putin probably believes that, as after his invasion of Georgia, his relations with the United States and its allies will be “reset” — sooner rather than later. The future of Ukraine and of global security depends on proving him wrong.