By Dean Yates

BAGHDAD, Nov 17 (Reuters) - Iraq is encouraged by signs of a thaw in ties between Iran and the United States over security in Iraq but wants the two sides to have a "proper dialogue" about the issue, the Iraqi government spokesman said on Saturday.

U.S. ambassador Ryan Crocker has held three rounds of talks with his Iranian counterpart this year on Iraqi security, easing a diplomatic freeze that lasted almost three decades. Crocker has said he expected more discussions soon.

A fourth round would follow the U.S. military's release this month of nine Iranian prisoners held in Iraq and comments by the U.S. military that unofficial assurances from Iran it would stop the flow of bombs into Iraq appeared to be holding.

"It's a good sign from both sides ... we want to encourage them to have a proper dialogue," spokesman Ali al-Dabbagh told reporters, suggesting Iraq wanted more than at previous sessions where the U.S. and Iran have traded accusations over who was to blame for the violence in Iraq.

Washington accuses Iran of arming, funding and training Shi'ite militias in Iraq. Tehran blames the sectarian violence, which has killed tens of thousands of Iraqis, on the U.S.-led invasion to topple Saddam Hussein in 2003.

Dabbagh said while the Iranians were showing restraint in Iraq, the government in Baghdad also wanted "negative" Iranian influences to stop. He did not give details.

Prime Minister Nuri al-Maliki had made Baghdad's position clear to Iran's most powerful figure, Supreme leader Ayatollah Ali Khamenei, Dabbagh said. Maliki told Khamenei "very frankly" that Iran had to choose between the Iraqi government or "any other party", Dabbagh said, without elaborating.

While Washington and Tehran remain divided over Iran's nuclear ambitions, U.S. officials have recently appeared to soften their rhetoric about Iran's involvement in Iraq.

A U.S. general said on Thursday that behind-the-scenes assurances from Shi'ite Iran to Iraq that the flow of weapons would stop appeared to be holding. Crocker last month noted a decision by Moqtada al-Sadr, head of the feared Mehdi Army Shi'ite militia, to call a ceasefire.

With Shi'ite Muslims now in power in Baghdad, ties have strengthened between the two oil-producing states since 2003. (Additional reporting by Mariam Karouny; Editing by Matthew Tostevin)

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