Kremlin critics condemned the move as a cynical manipulation and called for protests.
The resignations came hours after the president proposed new constitutional amendments to boost parliament's powers.
Kremlin watchers are trying to predict what will happen after Putin’s current six-year term ends in 2024.
U.S. sanctions have already pushed the ruble to 2-year lows.
More than 70 percent of voters backed him in an election in which he had no serious challengers.
The prime minister's comments came after Trump signed a bill imposing new sanctions.
A leading opposition figure's video claims to expose the prime minister's corruption.