WASHINGTON — The Senate Foreign Relations Committee approved on Thursday the most sweeping sanctions against Iran since the United States and five other nations reached an agreement with Tehran in 2015 to sharply limit that nation’s nuclear capability, and the committee warned Russia that it was almost certain to be the next target.

Because Iran has complied with the nuclear accord, the Senate committee had to find other reasons to impose the sanctions, and linked the penalties to Iran’s continued support for terrorism and its human rights violations, among other concerns. But the timing of the long-planned punishment was awkward, coming right after Iranians overwhelmingly re-elected President Hassan Rouhani, who has moved to expand personal freedoms in the country and integrate its economy with the West.

The Trump administration has supported new sanctions against Iran, which were approved 18 to 3 by the committee and could receive a full Senate vote as early as next month.

But Secretary of State Rex W. Tillerson had pleaded for more time before new sanctions were imposed on Russia, hoping to use the first few months of the Trump administration to fundamentally change a relationship he recently said had hit its lowest point in years.