The United States says it wants to have another face-to-face meeting with Iran over concerns that it is contributing to worsening security in Iraq.
The US accuses Iran of training militants
Iran had to stop supporting sectarian militias, said US state department spokesman Sean McCormack.
Iran's foreign minister said his country would respond positively to talks if requested by the US.
The two sides held a ground-breaking meeting in Baghdad in May - the first since they severed ties in 1979.
But the violence in Iraq has continued unabated since then - despite the sending of nearly 30,000 extra US troops there.
In the latest attacks, gunmen wearing military uniforms killed 29 people in a village in Diyala province north of Baghdad.
'Threat to troops'
"We think that given the situation in Iraq and given Iran's continued behaviour that is leading to further instability in Iraq, that it would be appropriate to have another face-to-face meeting... ," Mr McCormack told reporters.
"They need to stop supporting sectarian militias that are exacerbating sectarian tensions, they need to stop supporting EFP [explosively formed penetrators] networks that pose a threat to our troops," the spokesman said.
No date had been fixed yet.
Ambassadors to Iraq attended the talks in May
In Tehran, Foreign Minister Manouchehr Mottaki said: "We look positively at holding a second round of talks. There exists a possibility to hold such talks in the near future."
Early in July, the US military in Iraq accused Iran of orchestrating an attack that killed five US soldiers and of using Lebanese militants to train insurgents.
The information came from a top Hezbollah fighter recently captured in southern Iraq, an army spokesman said.
Brig-Gen Kevin Bergner said the suspect admitted working with the Quds Force, linked to Iran's Revolutionary Guards.
Iranian officials have always denied involvement in anti-US and anti-British attacks in Iraq.
Tehran says it supports the US-backed Iraqi government, and blames the violence on the myriad conflicts within the country since US-led forces toppled Saddam Hussein in 2003.
US envoy in Iraq Ryan Crocker met his Iranian counterpart Hassan Kazemi-Qomi for four hours on 28 May.
Both countries agreed that a secure and stable Iraq was in their interests.
But Iran rejected the US charge that it trained Iraqi militants, asserting that the coalition presence was an occupation.
The Iranians perhaps have most to gain from the talks with the US, says the BBC's Jon Leyne in Tehran.
Iran would like to use the talks to defuse the tension surrounding its nuclear programme and to prevent or delay new sanctions, our correspondent says.
Some officials in both Tehran and Washington would like to broaden the discussions to cover the many issues dividing the two countries, he says.
But holding any talks is hugely sensitive as, to many Iranians, America is still the great Satan.
To Americans, Iran is a state sponsor of terror with a president committed to the destruction of Israel, says our Tehran correspondent.