The first round seeking to end the bloodshed that broke out in Iraq after the United States overthrew Saddam Hussein four years ago but failed in its attempt to establish democratic rule there was held in Baghdad late May, and was in effect the first direct diplomatic contact between Washington and Tehran since 1979.
"To begin the second round of talks we are waiting for the American side to officially apply through the Swiss Embassy in Tehran [representing U.S. interests in Iran]," said Manouchehr Mottaki adding that Iraq had already asked Tehran to continue talks with Washington.
The four-hour talks between the U.S. and Iranian Ambassadors Ryan Crocker and Hassan Kazemi Qomi in the U.S.-controlled "Green Zone" in Baghdad ended in smiles May 28, but featured mutual accusations of supporting opponents and adversaries.
During the talks, the sides agreed to set up a trilateral committee on security that would help Iraq resolve security issues and strengthen the defense capability of the country.
The two sides agreed to support and strengthen the Iraqi government, which was another positive item achieved at the talks. The talks did not touch on the most controversial issue of bilateral relations - Iran's nuclear program - that the U.S. suspects is a covert weapons program.
Iraqi officials called for further discussion between the U.S. and Iran of security in Iraq, but some analysts in Iraq say it is the interference of the U.S. and Iran that has caused instability in the country.
Iran and the United States severed official relations following the 1979 seizure of the U.S. Embassy in Tehran by radical students in the wake of the Iranian revolution that toppled the Shah. American personnel were held hostage for 444 days.