The visit of the Iranian President to Iraq yesterday would have been unlikely - impossible even - without the US-led effort to topple Saddam Hussein. The war between Iran and Iraq, launched by Saddam in 1980, was one of the longest, bloodiest and most futile in history. It is one of the awkward facts of their modern history that America has brought the two closer together. The irony of this trip is that it is Mahmoud Ahmadinejad himself who has replaced Saddam as the object of fear within the region and concern in the wider world. While it has been Iran's disputed nuclear ambitions which have been the main focus of diplomatic conflict, this is not the only matter for which it has attracted suspicion. It continues, through its support for extremists, to be a disruptive influence in Israel-Palestine. It also casts a baleful shadow over Iraq.

This partly explains why Mr Ahmadinejad's trip could not have taken place sooner. Iran has officially stated its respect for the coalition administration in Baghdad while at the same time undermining efforts to create a stable security

situation in its neighbour. It has backed and built-up ultra-Shia elements, which Tehran believes that it can control, rather than more mainstream Shia figures, thus making reconciliation with Iraq's Sunni minority ever harder. And as the British Army is all too aware, Iran has been a menace in the area surrounding Basra, pouring arms and agents across the border. In the early months of last year, with the US military apparently exhausted and a new Democratic majority in Congress demanding a fixed timetable for the withdrawal of American troops, Tehran seemed convinced that it could secure its ideal outcome in Iraq - a Shia state, but a weak one.

The success of the US “surge” strategy since then has forced that assessment to be re-evaluated. On the whole, although its behaviour can be unpredictable, Iran has been less of a threat in the past few months than before. Tehran might have been responsible for some of the hardline factions seeking a ceasefire and compromise with more moderate Shia interests. Both Iraq's Kurdish President and its Shia Prime Minister appear to believe that Mr Ahmadinejad is not currently attempting to frustrate them. On that basis they have opted for dialogue with their neighbour, and Washington has not chosen to object to - and so in effect veto - his tour.

But Iraqi leaders need to tread carefully. It is far from clear whether Iran has decided that a stable and secure Iraq is actually in its interests or if it has merely determined that a strategy of subterfuge would not work at this moment and be counter-productive to its aim of easing the pressure at the UN over its nuclear activities.

Some of the heat on this score has been turned down since the surprisingly sweeping and very public American intelligence estimate that Iran was not actively pursuing the bomb was released last year. That intelligence analysis is certainly open to dispute and in any regard Iran continues to act as if it might make a dash for nuclear weapons in the future. Hence Tehran's reluctance to make the sort of concessions that would provide wholesale reassurance.

If Tehran is as benign in its intentions as it claims, then there are many steps that it could take which would convince others of this. In Iraq it could shift towards an unambiguous backing for the Government in Baghdad and assist the drive for national reconciliation. It could sever its destabilising links with the most radical Shias. This would not, of itself, prove that it did not want to acquire nuclear weapons. It would at least signal that Iran, too, wants peace and prosperity in the region to be the real legacy of the

appalling slaughter of the Iran-Iraq war and the demise of Saddam Hussein.