Spokesman John Kirby maintained the payment was negotiated separately from the release, but said it was withheld until the Americans had left Iran.
Five Americans held in Iran were released in January in exchange for seven detained Iranians.
The US airlifted $400m (£300.8m) worth of cash to Iran on the same day.
The exchange came as the US lifted international sanctions against Iran as part of the country's historic nuclear deal.
The timing of both incidents has prompted an outcry from Republicans, who accused the Obama administration of quid pro quo.
The White House, however, has pushed back on claims that the US paid a ransom for the release of the prisoners, saying the money was part of a longstanding financial dispute with Iran from before the 1979 Islamic Revolution.
"We were able to conclude multiple strands of diplomacy within a 24-hour period," Mr Kirby told reporters. "We deliberately leveraged that moment."
Mr Kirby's comments come after the Wall Street Journal reported that the release of the cash depended on the departure in Iran of the prisoners' plane.
The newspaper reported that US officials allegedly would not let a plane containing the cash in Geneva leave for Iran until a Swiss Air Force plane with the three of the US citizens on board left Tehran.