By Dean Yates

BAGHDAD, July 1 (Reuters) - Iraq is pressing the United States and Iran to hold a second round of talks in Baghdad to follow up a landmark meeting in May, but no date has been set, Iraq's foreign minister said on Sunday.

Hoshiyar Zebari also said the U.S. embassy in Baghdad had agreed to give Iran consular access to five Iranians who were detained by American forces in northern Iraq in January.

The U.S. military says the five are linked to Iran's Revolutionary Guards and backing militants in Iraq. Iran insists they are diplomats, wants them freed and has requested access.

U.S. Ambassador Ryan Crocker and his Iranian counterpart Hassan Kazemi-Qomi met in Baghdad on May 28 to discuss security in Iraq in what was the most high-profile meeting of the two arch enemies in almost three decades.

Both envoys described the talks as positive.

Iraq has invited both sides to meet again but neither have publicly said they would accept.

"We felt that there is a common interest in pursuing these talks, in having a second meeting, but no date has been agreed yet. We are working on that. There would be a second round, I hope so," Zebari told Reuters in an interview.

Washington accuses Iran of fomenting violence in Iraq, while Tehran blames the U.S.-led invasion in 2003 for sparking bloodshed that threatens to tear the country apart.

The May 28 discussions covered security in Iraq and both U.S. and Iranian officials say Iraqi issues, not other disputes, would be the focus of any further talks.

The United States and Iran are also at loggerheads over Tehran's nuclear programme. Washington says the atomic plans are aimed at building bombs, a charge Iran denies.

Zebari said he had raised the prospect of a second round of talks with U.S. officials during a visit to Washington.

"I found ... there is not unanimity of opinion on this but I think there is a strong school of thought there that supports the dialogue," Zebari said.

The agenda would be on the commitment and responsibilities both countries had toward Iraq's security, he said.

EASING TENSIONS

Zebari said he hoped the consular visit to the five Iranian detainees, who were detained in the Kurdish city of Arbil, would help ease tensions. There was no date for the visit, but it could happen any time, he said.

"We hope that would be a good gesture, a humanitarian gesture," he said, though he added he was no closer to getting the five freed, something he has sought for months.

He said he understood a U.S. military board would review the case of the five men only in October.

"We were hopeful a decision would be made in June, but now June is over and no decision has been reached," he said.

"From what we heard, it has been postponed until October. Then there will be a decision on their fate."

The five men have been visited by the International Committee of the Red Cross (ICRC). Iran for its part is holding three U.S.-Iranian citizens on security-related charges.

(Additional reporting by Mussab Al-Khairalla)

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