One message of President Trump’s is popular at home with his political base and embraced abroad by key Middle Eastern allies: The Islamic Republic of Iran is imperialist, repressive, and—unless we adopt a new strategy—on its way toward possessing nuclear weapons. To keep the threat at bay, Mr. Trump should take a page from the playbook Ronald Reagan used against the Soviet Union.

In the early 1980s, President Reagan shifted away from his predecessors’ containment strategy toward a new plan of rolling back Soviet expansionism. The cornerstone of his strategy was the recognition that the Soviet Union was an aggressive and revolutionary yet internally fragile regime that had to be defeated.

Reagan’s policy was outlined in 1983 in National Security Decision Directive 75, a comprehensive strategy that called for the use of all instruments of American overt and covert power. The plan included a massive defense buildup, economic warfare, support for anti-Soviet proxy forces and dissidents, and an all-out offensive against the regime’s ideological legitimacy.

Mr. Trump should call for a new version of NSDD-75 and go on offense against the Iranian regime. The administration would be wise to address every aspect of the Iranian menace, not merely the nuclear program. President Obama’s myopic focus on disarmament paralyzed American policy.

Under Mr. Obama’s deeply flawed nuclear accord, Tehran does not need to cheat to reach threshold nuclear-weapons capabilities. Merely by waiting for key constraints to sunset, the regime can emerge over the next decade with an industrial-size enrichment program, a near-zero breakout time, an easier clandestine path to a nuclear warhead, long-range ballistic missiles, access to advanced conventional weaponry, greater regional dominance, and a more powerful economy, increasingly immunized against Western sanctions. You could call this scenario the lethal Iranian end-state.