On Saturday, Crocker was circumspect when asked about prospects for further meetings.
"It's going to start with one meeting and see how it goes," Crocker said. "We're coming prepared to talk about Iraq."
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."
Many small issues could cloud the talks before they begin. There were US Navy exercises in the Persian Gulf last week and tough talk from President Bush about new UN penalties against Tehran over its nuclear program. The United States says Tehran is trying to build a bomb, while Iran says it needs nuclear technology for energy production.
Further complicating the talks, Iran said Saturday that it had uncovered spy rings organized by the United States and its Western allies.
Iran accuses the US of improperly seizing five Iranians in Iraq this spring. The US military is holding the five. Iran says they are diplomats; Washington contends they are intelligence agents.
The US also has complained about the detention or arrest of several Iranian-Americans in Iran in recent weeks. State Department spokesman Tom Casey said that issue was not on the US agenda for Monday.
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 US military power off its coast, almost refused to come.