Sullivan’s comments on Tuesday marked a rare public expression of confidence from Washington that the prisoner swap would take place.
“We believe that things are proceeding according to the understanding that we’ve reached with Iran,” Sullivan told reporters during a conference call.
“I don’t have an exact timetable for you because there [are] steps that need to yet unfold. But we believe that that remains on track,” he added.
Several news outlets reported earlier this month that Washington and Tehran were working on a deal to release the five American citizens in exchange for allowing Iran to access $6bn in funds that have been frozen in South Korea due to US sanctions.
The tentative agreement would also see the administration of US President Joe Biden free several Iranian nationals imprisoned in the United States.
But US officials previously cautioned that the deal had not been finalised.
Last week, Secretary of State Antony Blinken welcomed Iran’s decision to move the detained Americans from prison to house arrest as a “positive step”, but he stressed that “they are not home yet”.
On Monday, Iran’s Foreign Ministry Spokesperson Nasser Kanaani said no specific timeline had been set for completing the exchange, but that “it will take a maximum of two months for this process to take place”.
Experts welcomed the announcement as an important step, but said it does not fundamentally shift the US-Iran relationship.