By Sadeq Saba
Iran affairs analyst, BBC News
Presidents Talabani (l) and Ahmadinejad (r) met in November
The Iraq Study Group has recommended that the United States should engage with Iran as part of efforts to stem the violence in Iraq.
But there is a limit as to what Iran can do to stabilise its neighbour.
There is no doubt that Iran has influence over the moderate Shia and Kurdish groups who dominate the current Iraqi government.
The largest Shia party - the Supreme Council for the Islamic Revolution in Iraq (Sciri), led by Abdel Aziz al-Hakim - was based in Iran during Saddam Hussein's rule, and the Iraqi Prime Minister Nouri Maliki's Dawa party has had close relations with Iran.
Iraq's Kurdish President, Jalal Talabani, is also an old friend of Tehran.
But the violence in Iraq is not believed to be coming from these groups.
Calls for restraint
Most of the insurgents belong to militant Iraqi and foreign Sunni groups over which Iran does not appear to have any influence.
And the militant anti-American Shia cleric, Moqtada Sadr, is not seen as an ally of Iran and is partly motivated by Arab nationalism.
It is true that some ordinary Shias are involved in sectarian violence but it does not seem that Iran can stop them.
These people are not even listening to Iraq's most prominent Shia cleric, Ayatollah Ali Sistani, whose repeated calls for restraint have been ignored.
It appears that the idea of dialogue with Iran should rather be seen as a proposal for a more pragmatic US foreign policy towards the Middle East in general, and in particular the Israeli-Palestinian conflict.
In that context, Iran - with its huge influence on Islamic groups in Lebanon, Iraq and the Palestinian territories - can play a major role.
The American panel is also aware that if Tehran cannot turn down the heat in Iraq, it certainly can turn it up.