WASHINGTON—As an embattled Nicolás Maduro clings to power in Venezuela, the Trump administration has deadlocked over one of its remaining options for bolstering the opposition and pressuring Mr. Maduro, according to American officials and an administration email exchange.

Some in the Trump administration and supporters of its policy toward Caracas are concerned that momentum is slowing in the push to pry Mr. Maduro from power, despite efforts to impose increasingly dire sanctions on the Venezuelan government and rally support...