WASHINGTON—Senior Justice Department officials objected to sending a plane loaded with cash to Tehran at the same time that Iran released four imprisoned Americans, but their objections were overruled by the State Department, according to people familiar with the discussions.

After announcing the release of the Americans in January, President Barack Obama also said the U.S. would pay $1.7 billion to Iran to settle a failed arms deal dating back to 1979. What wasn’t disclosed then was that the first payment would be $400 million in cash, flown in at the same time, as The Wall Street Journal reported Tuesday.

The timing and manner of the payment raised alarms at the Justice Department, according to those familiar with the discussions. “People knew what it was going to look like, and there was concern the Iranians probably did consider it a ransom payment,’’ said one of the people.

The disclosures reignited a political furor over the Iran deal in Washington that could complicate White House efforts to fortify it before Mr. Obama’s term ends.

Three top Republicans who have been feuding in recent weeks—presidential candidate Donald Trump, Sen. John McCain and House Speaker Paul Ryan—were united Wednesday in blasting the Obama administration.