US Secretary of State John Kerry said Sunday a deal with Iran could be brokered within months if Tehran proves that its nuclear program was not being used to build atomic weapons.

In an interview with CBS's "60 Minutes" program, Kerry said the stated desire by Iranian President Hassan Rouhani for an agreement within three to six months could be met sooner if Iran satisfied certain conditions.

"It's possible to have a deal sooner than that -- depending on how forthcoming -- and clear Iran is prepared to be," Kerry said.

"We need to have a good deal here. And a good deal means that it is absolutely accountable, failsafe in its measures to make certain this is a peaceful program.

"If it is a peaceful program, and we can all see that -- the whole world sees that -- the relationship with Iran can change dramatically for the better and it can change fast," Kerry added.

The United States would not consider lifting sanctions against Iran until it was clear that a "verifiable, accountable, transparent process" was in place, the top US diplomat said.

He said opening up an underground nuclear enrichment facility in the mountains near the city of Qom for international inspection would demonstrate that Iran had no nuclear weapons ambitions.

"They could immediately open up the inspection of the Fordow facility, a secret facility underground in the mountains," Kerry said.

"They could immediately sign the protocols, the additional protocols of the international community regarding inspections.

"They could offer to cease voluntarily to take enrichment about a certain level, because there's no need to have it at a higher level for a peaceful program."

Kerry's comments came amid a marked improvement in relations between Washington and Tehran in recent months that culminated in a landmark telephone conversation between Rouhani and US President Barack Obama on Friday.

The nascent rapprochement has raised the prospect of an agreement being reached about Iran's nuclear program.

Western countries have long insisted Iran is secretly developing nuclear weapons; Iran insists the program is entirely peaceful in nature.