Washington (CNN)_Secretary of State John Kerry acknowledged Tuesday that the Iran nuclear deal most likely won't require the country to detail suspected past efforts to develop a nuclear weapon, a concession sought by Tehran.

"We are not fixated on Iran specifically accounting for what they did at one point in time or another," Kerry told reporters Tuesday by remote video from Boston, where he has been recuperating from a broken leg.

"We know what they did," Kerry added. "We have no doubt. We have absolute knowledge with respect to the certain military activities they are engaged in. What we are concerned about is going forward."

His comments downplayed a long-standing demand by world powers that Iran come clean about any past efforts to develop a military dimension to its nuclear program. U.S. officials and European diplomats previously pledged that sanctions relief would be tied to Iran answering lingering questions from the International Atomic Energy Agency, the UN nuclear watchdog.

The United States and five other world powers are negotiating with Iran to curb the country's nuclear program and keep it from building a nuclear bomb, though Iran insists that its nuclear program is peaceful.

Sanctions relief for Tehran and the level of access inspectors will have in Iran continue to be major sticking points in the final negotiations, which diplomats say are getting increasingly difficult as diplomats stare down a fast-approaching June 30 deadline.

A preliminary deal reached in April, which provides a framework to hash out the details of the final agreement, said Iran "will implement an agreed set of measures to address the IAEA's concerns regarding the possibility military dimensions (PMD) of its program" in a final pact.

"It will be part of a final agreement. It has to be," Secretary of State John Kerry told PBS in an interview in April after the interim deal was reached. "If there's going to be a deal, it will be done."

Iran has denied it has engaged in covert efforts to develop warheads and delivery systems but has yet to grant the UN nuclear agency access to nuclear scientists or suspicious sites.

Western diplomats are also pushing for the deal to include unprecedented levels of access in which international inspectors could visit any facility in Iran suspected of nuclear activity, including military sites like the Parchin military installation.

U.S. officials and European diplomats said access to those sites remains one of the main sticking points in negotiations. Tehran has strongly pushed back on that level of access, looking to keep military sites off limits.

U.S. officials and European diplomats on Tuesday resisted suggestions that they were now backtracking on the issue of Iran's past military-related activity, saying that issue never had to be resolved in order for the deal to be reached.

"As part of a comprehensive agreement, we want the IAEA to be able to do its work to resolve possible past military dimensions of Iran's program, and they will have to give the IAEA the access it needs to do its job," a senior administration official told CNN Tuesday.

The sources stressed because the IAEA must verify Iran is not currently working to develop a nuclear weapon, it will need Iran to answer some questions about past military-related activity.

"It's not about Iran doing some mea culpa. We have never been about that and they are never going to do that. So hinging a deal on some confession is not realistic and not even necessary," one Western diplomat said. "But in order to satisfy ourselves now that the program is peaceful we will need access to sites and individuals that have been used in the past.

Last week IAEA chief Yukiya Amano confirmed that the agency would not be able to satisfy remaining questions about Iran's past atomic work before the deadline for the deal at the end of the month.

Amano did say, however, that Iran has committed to providing inspectors access nuclear sites, even though as recently as last month Supreme Leader Ayatollah Ali Khamanei pledged "no inspection of any military site and interview with nuclear scientists will be allowed."

Kerry said Tuesday that sanctions relief would be tied to Iran satisfying international concerns about Iran's future atomic weapons activities.

Iran wants near immediate sanctions relief once the deal is reached, while Western officials are wary of lifting sanctions too quickly as they keep an eye on Tehran's activities in the early months after a deal is reached.

"It is critical to us to know that going forward those activities have been stopped. And that we can account for that in a legitimate way," Kerry said. "In order to have an agreement to trigger any kind of material, significant sanctions relief, we would have to have those answers."

The U.S. and its negotiating partners -- Britain, France, Germany, Russia and China -- are meeting this week with Iranian officials in Vienna to continue negotiations. Kerry is expected to travel to Vienna next week for the final round of talks before the June 30 deadline.

"The talks remain tough," Kerry said. "And just as I have said consistently, we're not going to rush to an agreement for the sake of an agreement, and we're not going to sign an agreement that we don't believe gets the job done."

By CNN