TEHRAN, Aug 19 (Reuters) - Iranian President Mahmoud Ahmadinejad has accepted an invitation to visit neighbouring Iraq, Iran's foreign minister said on Sunday, a move that would be unlikely to be welcomed by the United States.

Foreign Minister Manoucher Mottaki said Iraqi Prime Minister Nuri al-Maliki had invited Ahmadinejad after Maliki visited Tehran on Aug. 8-9, but added a final decision had yet to be taken.

"When a definite decision about the trip is made, the timing will be announced to the public," Mottaki told reporters in the northeastern city of Mashhad, according to the ISNA news agency.

With Shi'ite Muslims now also in power in Baghdad, ties have strengthened between the two oil-rich states since 2003, when U.S. forces toppled Iraqi President Saddam Hussein, a Sunni Arab who waged an eight-year war against Shi'ite Iran in the 1980s.

The U.S. military accuses the Islamic Republic of arming and training militias behind some of the violence ravaging post-Saddam Iraq.

Iran rejects the charge and blames the presence of U.S. forces, numbering about 162,000, for the mayhem.

Tehran and Washington, which have not had diplomatic ties since shortly after Iran's 1979 Islamic revolution, are also at loggerheads over its disputed nuclear programme. Iran denies Western accusations it is aimed at building atom bombs.

Baghdad has urged both Iran and the United States to negotiate and not fight out their differences on Iraqi soil, and the two arch-foes held landmark talks in Baghdad in May and July on ways to improve security in Iraq.

Some analysts say the two old foes, despite their mutual accusations, have a shared interest in ending the violence in Iraq. Iran wants a friendly government running a stable country while a secure Iraq would enable the United States to pull out.

Mottaki said that in regard to the existing situation in Iraq, the two sides' "attitude had become very logical and realistic", ISNA said.

"We understand America's conditions in Iraq," he was quoted as saying, suggesting the outcome of the talks would depend on coming up with practical steps and correcting U.S. policies there. "In this regard we are not without hope."

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