Diplomats said on Friday that Iraq's interest in seeing a meeting between Condoleezza Rice, the US secretary of state, and Manouchehr Mottaki, the Iranian foreign minister, was clear.
Iraq acknowledges Iran is an influential force both as a neighbour and for its links with the Iraqi government.
But the diplomats, who declined to be named, said Iran was holding out against substantial contacts with Rice, although she and Mottaki exchanged what US officials described as pleasantries over lunch on Thursday.
Ryan Crocker, the US ambassador to Iraq, did not rule out a meeting between Rice and Mottaki.
"We are just going to take it as it goes. We will see ... what options present themselves," Crocker told reporters.
"The point from our side is not to have meetings with the Iranians. It is what can we do in Iraq and what can we do in the region to create better circumstances and a better future for the Iraqis."
While Rice and Mottaki exchanged greetings during lunch on Thursday, they did not have further contact at dinner.
Talks between Rice and Mottaki would be one of the highest-level US-Iran contacts since a 1979 revolution turned Iran from a close US ally into the arch-foe Islamic Republic.
Border security
Over the years Iran has been the less enthusiastic on dialogue. Iraq has met its neighbours several times over the past three years and has received promises of co-operation on border security but says armed groups are still able to smuggle fighters and weapons into the country.
Baghdad depends on US military support in its drive to halt a slide into all-out civil war by stamping out sectarian violence. Washington has accused Iran of fomenting violence in Iraq. Tehran says it does not.
At the conference on Friday, Iraq's neighbours as well as ministers from the Group of Eight leading industrialised nations and the European Union will discuss how to stabilise the country.