Kazemi-Qomi said Iran saw "positive" steps in the talks.
"Some problems have been raised and studied and I think this was a positive step ... In the political field, the two sides agreed to support and strengthen the Iraqi government, which was another positive item achieved in these talks," he told state television.
Crocker said the Iranians had proposed setting up a mechanism with Iranian, US and Iraqi participation to co-ordinate on Iraq's security. He said he would refer the proposal to Washington.
Kazemi-Qomi told reporters that Iran had offered to help train and arm Iraq's military.
From Tehran, Manouchehr Mottaki, Iraq's foreign minister, left open the possibility of future meetings with the US but only if Washington admitted its war in Iraq and other regional issues have not been successful.
"We are hopeful that Washington's realistic outlook toward the current issues in Iraq, a confession about its failed policy there and the region as well as an indication of determination to change the policy would guarantee the success of the current talks and possible further negotiations."
Crocker said that "the Iranians did not go into any great detail" during the meeting at the home of Nuri al-Maliki, the Iraqi prime minister, in Baghdad's fortified Green Zone.
'Opening of a door'
"They made the assertion that the coalition presence was an occupation and the effort to train the Iraqi security forces had been inadequate to the challenges."
"Let the people of Iraq vote if they want the US to stay or leave"
Bob Kaye, Bohemia, US
Send us your viewsIt was the first high-level meeting between the two countries for 27 years. Iraqi officials also attended the meeting.
Al-Maliki told both sides that Iraqis want a stable country free of foreign forces and regional interference.
He also said that the US-led forces in Iraq were only here to help build up the army and police and the country would not be used as a launching ground for a US attack on its neighbours - a clear reference to Iran.
Hoda Abdel-Hamid, Al Jazeera's Iraq correspondent, said that the meeting should be viewed as the "opening of a door".
"Both parties are deeply suspicious of one another. The issues are complicated and intertwined, so you can't look at the Iraq situation without looking at broader regional issues.
"Publicly, the US wants Iran to stop training and providing the Shia militias with weapons, and logistical and financial support [and] Iran wants a US timetable for troop withdrawal from Iraq.
"Iran has some of the strongest political and economic ties in Iraq.
"[But] Iraq also needs the US at this stage because of its security situation. It cannot take care of security issues by itself," she said.
Hoshiyar Zebari, the Iraqi foreign minister, said: "I think it is a positive development. We should encourage it and build on it. This is just the beginning of the process."
Iran's nuclear programme, which Washington believes to be a bid for developing atomic weapons, was not discussed. at the meeting.
Crocker said that the US expected Iran to propose a second meeting on Iraq.
As the meeting ended, a truck bomb exploded outside one of Baghdad's most revered shrines in the business district of Sinak, killing at least 19 people and damaging the Abdel Qadir Gilani Mosque.