During a meeting that U.S. Ambassador Ryan Crocker described as businesslike, the American said he told the Iranians their country needed to stop arming, funding and training the militants.
"This is about actions, not just principles, and I laid out to the Iranians direct, specific concerns about their behavior in Iraq and their support for militias that are fighting Iraqi and coalition forces," Crocker told a Green Zone news conference.
The American said Iran proposed setting up a "trilateral security mechanism" that would include the United States, Iraq and Iran. Crocker said the proposal would need study in Washington.
Hassan Kazemi Qomi, the Iranian envoy, also said that he told the Americans that Tehran was ready to train and equip the Iraqi army and police to create "a new military and security structure."
Kazemi did not elaborate nor would he say how Crocker responded.
After the meeting, Kazemi said a number of positive steps were taken, reports CBS News chief foreign correspondent Lara Logan.
But just a short distance away from the talks, a massive car bomb exploded outside one of Iraq's holiest Sunni mosques, killing more than twenty people and injuring dozens more.
The violent and political turmoil in Iraq has escalated to the point where it's achieved something nothing else could in more than 25 years: to bring the United States and Iran together in formal talks for the first time since the Iranian Revolution in 1979.
Washington wants Tehran to butt out of the conflict here, while Tehran wants the United States out of Iraq completely, adds Logan.
So far there's no sign the U.S. ambassador is willing to do what Iran wants: admit that American policy in Iraq and the Middle East region has been a failure, and set a date for withdrawal of U.S. forces.
Washington believes Iran is implicated in attacks on U.S. troops because they're supplying weapons and fighters to kill Americans in Iraq. Their major concern is EFPs (or explosively formed penetrators), sophisticated armor-piercing bombs which the United States says can only be made in Iran.
Another issue dividing the two countries is the fate of seven Iranians in U.S. custody. Five of them were arrested during a raid on an office in the northern Iraqi city of Irbil in February.
In the days leading up to these talks, Tehran increased tensions by arresting several Iranian-Americans and accusing the United States of setting up a spy ring in the region. Not up for discussion in today's talks but complicating the U.S.-Iran relationship right now are even bigger issues, primarily Iran's nuclear program and fears in Tehran that the Bush administration is planning regime change in Iran, the same way it removed Saddam Hussein from power.
Washington and its Sunni Arab allies, on their side, are deeply unnerved by growing Iranian influence in the Middle East and the spread of increasingly radical Islam.
Compounding all that is Iran's open hostility to Israel.
Regardless, the Baghdad talks are the first of their kind and a small sign that Washington thinks rapprochement is possible after nearly three decades of animosity. Iran, angry over the blunt show of U.S. military power off its coast, almost refused to come.
Iraqi officials said the meeting between Crocker and Kazemi was cordial and focused solely on Iraq.
"There are good intentions and understanding and commitment between the two countries," Ali al-Dabagh, an Iraqi government spokesman, told reporters.
Crocker concurred: "There was pretty good congruence right down the line and support for a secure, stable, democratic federal Iraq, in control of its own security, at peace with its neighbors, he said.
There were no breakthroughs today, adds Logan, but the door was left open for future meetings. The Iranians showed they want more talks, but the United States signaled it wants to see a change in Tehran's behavior before agreeing to come back to the table.
The talks were held at Iraqi Prime Minister Nouri al-Maliki's office in the Green Zone compound in Baghdad. Iraq was being represented at the talks by National Security Adviser Mowaffak al-Rubaie.
"U.S.-Iran talks come at a time when bilateral relations have nose-dived because of Iranian defiance on its nuclear program and the evidence that has surfaced regarding aid to Shiia insurgencies in Iraq, but it is, nonetheless, a landmark meeting," said CBS News foreign affairs analyst Pamela Falk.
Just before 10:30 a.m., al-Maliki greeted the two ambassadors, who shook hands, and led them into a conference room, where the ambassadors sat across the table from each other. Al-Maliki then made a brief statement and left the room.
"We are sure that securing progress in this meeting would, without doubt, enhance the bridges of trust between the two countries and create a positive atmosphere" that would help them deal with other issues, he said.
Speaking in Tehran, Iranian Foreign Minister Manouchehr Mottaki said Monday the talks could lead to future meetings, but only if Washington acknowledges that its Middle East policy has not been successful.
"We are hopeful that Washington's realistic approach to the current issues of Iraq by confessing its failed policy in Iraq and the region and by showing a determination to changing the policy guarantees success of the talks and possible further talks," Mottaki said.
Monday's talks were to have a pinpoint focus: what Washington and Tehran — separately or together — could do to contain the sectarian conflagration in Iraq.
"The American side has accusations against Iran and the Iranian side has some remarks on the presence of the American forces on Iraqi lands, which they see as a threat to their government," al-Dabagh said in a briefing to reporters during the closed-door meeting.
Will this first meeting, as the Iraqis openly hope and as the Iranians and Americans may quietly aspire, be sufficiently cordial and productive that a second meeting becomes possible? Should that happen, will a future dialogue involve higher-level officials, perhaps Secretary of State Condoleezza Rice and Iran's foreign minister?
The U.S. ambassador disclosed that the Iranians said they would propose a second session.
"We will consider that when we receive it," Crocker said. "The purpose of this meeting was not to arrange other meetings."
A political aide to al-Maliki told The Associated Press that Iraq hoped to play a mediator's role in easing tensions between the Americans and Iranians, which Iraqi officials have routinely said are being played out in Iraq.
The adviser, who spoke on condition of anonymity because he was not authorized to speak on the matter, said Iraq would remain neutral as regards to its position in the disputes.
"But we want to try to close the gap, to be partners in the dialogue," the official said. "It is time to look forward, not backward."