TEHRAN — Iran and Boeing signed a deal for the sale of 80 airplanes on Sunday, five weeks before the inauguration of President-elect Donald J. Trump, whose Republican supporters in Congress have tried to block any aircraft sales to Iran.

Iran’s national airline, Iran Air, said that it had signed an agreement with Boeing, an American manufacturer, to purchase the aircraft, at a total cost of $16.6 billion.

In September, the Treasury Department gave approval for Boeing and its European competitor, Airbus, to sell planes to Iran.

Boeing confirmed the deal, saying that the contract was reached within the terms of the government license that the department had issued.