"From what we see, we believe that it is doing that," Theresa May told CBS.

"We believe that that should stay in place. And others, involved in putting that deal together believe that it should stay in place," May said in excerpts of an interview shown on "Face the Nation" that was to air in full Monday on "This Morning."

But there are other issues outside the deal that also need to be dealt with, she said.

"Looking at the issue of ballistic missiles. Looking at -- the way in which -- Iran is acting in the region -- to destabilize the region. We need to address those issues," May said.

May's interview came as world leaders geared up for a week of high-stakes diplomacy at the UN General Assembly, which is set to be dominated by North Korea and Iran.

On Wednesday, President Donald Trump will for the first time chair a Security Council meeting on non-proliferation and weapons of mass destruction that will focus heavily on Iran -- likely triggering a clash with other big powers.

Earlier this year, Trump pulled the US out of the deal it reached with Iran and five other countries in 2015. That accord lifted sanctions against Tehran in exchange for restrictions on its nuclear program.

Now, the US is reimposing those sanctions.

Other parties to the deal have argued that it is working and should stay in place, while the International Atomic Energy Agency has said Iran is complying with the accord.