Significant gaps remain between international negotiators and Iran over its nuclear program, but talks that began early this year are “getting down to the serious business” and the drafting of a comprehensive agreement will begin in May, a senior Obama administration official said Friday.

“I’m absolutely convinced that we can” complete a deal by a July 20 deadline, the official said, “although the real issue is not whether you can write the words on paper . . . it’s about the choices that Iran has to make. Some of them are very difficult.”

The official spoke as high-level negotiators prepared to return next week to Vienna for a third round of talks between Iran and group known as the P5+1 — the five permanent members of the U.N. Security Council (the United States, Britain, China, France and Russia) plus Germany. The European Union also is participating in the negotiations.

In November, the parties agreed to a plan for negotiating a long-term deal to define the scope of Iran’s nuclear program and ensure that it cannot build a weapon, in exchange for lifting international economic sanctions.

To show good faith during the talks, Iran froze parts of its nuclear program and the West provided some temporary sanctions relief.

Negotiations that began Jan. 20 are to be completed within six months, although the agreement allows for an extension if progress is being made.

Negotiators on all sides have publicly praised the substance and seriousness of the talks, including Undersecretary of State Wendy Sherman, the chief U.S. negotiator, and Iranian Foreign Minister Mohammad Javad Zarif.

Outside of the closed-door sessions, however, there have been calls in the United States and Iran for a hard line. Some Iranian leaders have said that they will never give up a heavy-water reactor and the ability to enrich uranium — two paths to nuclear weapons material. Numerous lawmakers in the United States, along with Israel, have said that neither can be part of a final agreement, even under strict safeguards, because Iran cannot be trusted.

The senior official, speaking on condition of anonymity to brief reporters on administration views, brushed off those concerns. “We’re quite direct and quite straightforward with each other, so I don’t think there’s any mystery about positions. And what we are focused on is what is discussed in the room, not what anyone says on the outside.”

“We know where we can see points of agreement,” the official said. “We know where the gaps are that have to be bridged. But I’ve also said this is a Rubik’s Cube, and where one makes progress on one element may mean there’s more trade space on another element.”

The official declined to provide specifics about the negotiations but said that “nothing is agreed until everything is agreed, and I would add to that nothing is agreed till everyone agrees to it.”