Munzir Baig, Muscat, Oman
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"If we encounter each other, then I'm certainly planning to be polite, to see what that encounter brings," Rice said of a potential discussion with Manouchehr Mottaki, Iran's foreign minister.
Mahmoud Ahmadinejad, the Iranian president, expressed interest, too.
He said on Wednesday that Tehran would welcome talks with the US on the sidelines of the conference, the official Islamic Republic news agency reported.
Iraq has persuaded Egypt to drop a proposed call for a three-month ceasefire between fighters and security forces.
Hoshyar Zebari, Iraq's foreign minister, said his government strongly opposed the truce call because it would legitimise fighters opposing Iraqi and US-led forces.
Instead, the final document to be issued at the security conference in Egypt will make a general call for peace, Zebari said.
"This is legitimising, formalising, the Iraqi government, the elected government, with a bunch of terrorists and killers who are shadows, who are an unknown entity," Zebari said.
"That's why we insisted that this is not the right language to be used in an important document and instead there should be a call to all parties to end ... the senseless killing of ordinary citizens," he said.
The Egyptian ceasefire proposal had underlined the differences between Sunni-led Arab nations and the Shia-led Iraqi government.
Zebari said his Egyptian counterpart, Ahmed Aboul Gheit, had agreed to drop the ceasefire proposal and substitute "a general call to end violence" at a meeting on Tuesday.
'Everything at stake'
On Wednesday, Rice "Iraq's neighbours have everything at stake".
Iraq is at the centre of either a stable Middle East or an unstable Middle East."
The two-day conference is taking place amid unrelenting sectarian violence in Iraq and mounting concern by Iraq's neighbours, particularly Saudi Arabia, that Nuri al-Maliki, the Shia prime minister, is not committed to reconciliation and that the violence will spill over to neighbouring countries.
In the run-up to the landmark conference, Western and regional leaders have hammered home the same message that Iraq's influential neighbours need to do their share.
On Sunday, al-Maliki again warned his neighbours that the "terrorist attacks that target Iraq are not limited to Iraq, but will spread to every country in the world".
Egyptian police imposed a tight security cordon around Sharm el-Sheikh as the 27 foreign ministers and diplomats representing 22 other countries started arriving.