British Prime Minister David Cameron defended the landmark Iran nuclear agreement saying it was "better than the alternative" but said western powers would remain tough on Tehran over its close ties with Syria's Bashar al-Assad and its support to Houthi rebels in Yemen.

"I think if there wasn't a deal, I think we would face Iran with a nuclear weapon and that would have given a terrible choice to the West of either enabling that, allowing that to happen or a very difficult decision to take military action, so this is the better outcome," Cameron said during a taped interview that aired on NBC's Meet the Press on 19 July.

Iran and six major world powers reached a nuclear deal on 14 July, capping more than a decade of negotiations with an agreement that could transform the Middle East.

Addressing critics' concerns that the deal focused on Iran's nuclear program without addressing Iran's growing political influence in the region, Cameron said international allies "are not starry-eyed" about the Iranian regime and would continue to exert pressure on Iran and its policies in the Middle East.

"We shouldn't be naive or starry-eyed in any way about the regime that we are dealing with. I am certainly not. I spoke to President Rouhani yesterday and said we want to see a change in approach that Iran takes to issues like Syria and Yemen and to terrorism in the region and we want the change in behaviour that should follow from that change. So we are not starry-eyed at all and I would reassure our Gulf allies about that, but actually taking the nuclear weapon issue of the table, that is a success," Cameron said.

Opponents of the negotiations say it could still allow the Middle Eastern state to build nuclear weapons even if it complies with the deal.

"Well I don't believe that's right actually. This deal says that it's never acceptable for Iran to have a nuclear weapon. Obviously the time frame for which the safeguards are in place, the inspection is in place, is for a particular period of time, but the deal actually says it's not acceptable for Iran to have a nuclear weapon, but again what we have done is make sure that the timeline for them possibly getting a nuclear weapon has got longer, not shorter," Cameron said.

The agreement is a political triumph for both Obama, who has long promised to reach out to historic enemies, and Rouhani, a pragmatist elected two years ago on a vow to reduce the isolation of his nation of 80m people.