Despite a thin, lingering cloud of buts and maybes, the deal concluded between Iran and six leading countries over Tehran's nuclear programme in the small hours of Sunday morning was historic – the kind of diplomatic agreement that alters the political landscape, forces at least some of the intransigent to change their positions, and opens up new opportunities that previously seemed hopelessly far-fetched.

The core of the interim deal is that Iran has agreed to suspend uranium enrichment above the 5% level (pending a final settlement to be negotiated within the next six months) in exchange for relaxation of some sanctions – a relaxation estimated to be worth $7bn to Iran ("modest", according to the US).

In addition, the Iranians have agreed to begin converting uranium enriched to a higher level to put it beyond weapon use, to increase the frequency and intrusiveness of inspections, to suspend work on the Arak plutonium plant, and to halt development of improved centrifuges that would greatly increase the speed and efficiency of enrichment.

Initially, some reports noted an apparent difference of view post-deal – the Iranians were claiming it recognised Tehran's right to enrich uranium, while the US and others were saying that it had done no such thing. As with many diplomatic ambiguities, both are right, and both wrong. No such statement appears in the deal in those terms, but it does provide for Iran to continue enrichment below the 5% level (consistent with "peaceful purposes"), subject to conditions and the still-to-be-negotiated final settlement.

It soon emerged that the Iranian negotiators had full backing for the terms they had agreed – President Hassan Rouhani and, more important, the supreme leader, Ayatollah Ali Khamenei, quickly issued statements welcoming it. Khamenei said: "God's grace and the support of the Iranian nation were the reasons behind this success." Khamenei's acclaim should ensure that the voices of dissenting hardliners in Iran will be muted.

The blast of disapproval for the deal from the Israeli prime minister, Binyamin Netanyahu, will also help quieten dissent within Iran. President Obama has already decided he can face down both Israeli and Saudi opposition. But he does have to persuade Congress and others to give this process a chance, and not impose new sanctions. To this end Obama and his colleagues are presenting the deal as a "first step" that halts or reverses Iran's nuclear programme. The US would be wise to avoid any tendency towards triumphalism, but the deal does represent real progress towards making safe the Iranian nuclear enterprise. Signed off by seven of the world's most important foreign ministers, it nonetheless also signifies international recognition of Iran as a major nuclear power.

Part of the significance of the deal is that both the US and Iran have pulled back from positions of intransigence, confrontation and escalation. The Iranians could have remained obdurate against any kind of concessions or limits on their nuclear programme, accepting the price of isolation and the massive economic damage from sanctions, and making life miserable for their people. The US could have continued with the "no enrichment, can't trust Iran" line, steadily increasing the sanctions' pressure until the only sanctions left to apply were military ones.

It is a mistake for Netanyahu, the Saudis or anyone else to suggest that would have been the right course. Things may yet go wrong, but it must be right to give the delicate seedlings of trust and diplomacy a chance. It involves risk, and courage, but it is the kind of risk that, ultimately, politicians are paid to take. After a decade and a half of interventionist wars, American, British and other servicemen and their families have a right to demand that diplomats and politicians exhaust all avenues of negotiation before we resort to military options.

In the continuing talks, the Iranians will look for an explicit statement of their right to enrich uranium, and the six will look for tight safeguards to prevent the Iranians engaging in weapons-related development. The US will also, doubtless, look for new commitments from the Iranians to soften their stance on Israel.

Meanwhile, we should not overlook the internal political situation in Iran. Ultimately, improvements in the political and human rights fields are up to the Iranians. But an Iran that is engaged with the outside world is more amenable to influence in the right direction than one that is isolated and shouting at the rest of the world through a megaphone, à la Mahmoud Ahmadinejad.