We should assume that President Mahmoud Ahmadinejad does not intend much change in the next four years of his presidency. Why would he? He has campaigned on a promise of more of the same.

Dismissing the evidence of the “green wave” which swept over Iran in the past few weeks, he now claims he has a mandate to deliver just that.

Can he, nonetheless, be given reason to change, a bit? That is what US foreign policy will now test — and, with far less influence, British and Israeli, too.

However, the first test will come from Iranians themselves. Ahmadinejad may have found it far easier than his critics in the West hoped to secure this election, however he did it (and what this has demonstrated, in case it were in any doubt, is that the support of the Supreme Leader is decisive). But he may find it far less easy to run Iran with the heavy hand of the past four years.

Whether the supporters of Mir Hossein Mousavi manage to put up a sustained protest will be clearer after the next 48 hours. The widespread arrests of opposition figures, the brutality with which the celebrations of his victory were conducted, and the calculated attempt to “take back” northern Tehran, the affluent, middle-class stronghold of Mousavi, suggests that, with good reason, Ahmadinejad’s opponents may choose to lie low.

But almost certainly the demonstrations of the past few weeks have changed Iran. They have shown, to Iranians and to the world, the depth of the opposition to the religious establishment’s social repression, particularly among the young and educated, who are also appalled at the isolation which Ahmadinejad has brought.

Some of those young people will leave, and Iran will be narrower and more isolated because of it. But others will stay and continue to test the regime’s weaknesses. If the President tries to sustain the interruption to mobile and internet services which mysteriously happened on polling day, he will be taking on the generation which has made Facebook, YouTube and Twitter the means of political expression.

He may also have trouble with the poor, the bedrock of his support, particularly if the results were rigged and his support here is lower than the declared figures suggested.

His promise to keep food and fuel prices low is a huge strain on the budget, with oil prices still well down from their high.

These are the weak points of the Ahmadinejad regime, and so the targets for American foreign policy.

On the nuclear front, it would be prudent to assume that Ahmadinejad intends no change in the status quo: that he wants to keep stalling the inspectors from the International Atomic Energy Agency, the United Nations watchdog, while pressing ahead with work which could soon give Iran a nuclear weapon, as well as the fuel for reactors which he claims is the only goal. He has not, after all, given an inch to diplomacy since his 2005 election.

President Barack Obama has given Iran a deadline of the end of the year for negotiations on the nuclear front. He hasn’t said whether a military strike might be an ultimate option, and at this point, doesn’t need to.

The best course now will be to raise the stakes in that diplomacy, offering Iran all kinds of commercial and cultural connections to the wider world if it amends its programme, while threatening even tougher sanctions if it does not. Iranians, as this election showed, are sensitive to that prestige, and hurt by the isolation and opprobrium they now encounter abroad.

For that, Obama will need the help of Germany and Italy, the biggest trading partners of Iran within Europe, and the least helpful so far in supporting sanctions. Their slow-motion obstruction has been, in its way, more damaging to the effort to put pressure on Iran than the showy blocking votes of Russia and China in the UN Security Council.

On the Israeli-Palestinian conflict, Obama has made the right move already, by restoring the US claim to be an even-handed broker, and by showing his determination to try to resolve that conflict. That will not stop Iran supporting, with cash and arms, the militias of Hezbollah and Hamas. But it will help to dilute, a tiny bit, the view that this is a noble cause.

Ahmadinajad is not a leader who is for turning. Few who claim validation by auras of bright lights and spiritual messages are that. But it should be possible for Obama to make Iran an offer, visible to the world, which puts him in a very difficult position at home if he turns it down.

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