(Adds U.S. reaction, possible Ahmadinejad visit)

By Paul Tait

BAGHDAD, Aug 19 (Reuters) - French Foreign Minister Bernard Kouchner arrived in Baghdad on Sunday on the first visit by a top French official to Iraq since the beginning of the U.S.-led war in 2003 which France vigorously opposed.

Kouchner's arrival in Baghdad coincided with President Nicolas Sarkozy's return from a holiday in the United States which was seen as an effort to improve relations with U.S. President George W. Bush after a bitter fallout over the war.

Kouchner, invited to Baghdad by Iraqi President Jalal Talabani, told a news conference he was on a listening visit and had not come to present any diplomatic initiative.

"I want to listen to the people ... We have to understand this country, we have to understand what's going on between the Shi'ites and the Sunnis, not only in Iraq," he said.

Kouchner told the joint news conference with Iraqi Foreign Minister Hoshiyar Zebari that there was no military solution in Iraq and there had to be a political one.

"Now we have to face the reality, including the American view ... but this is an Iraqi problem and it must be solved by the Iraqis," Kouchner said.

Kouchner said he was to meet representatives of all of Iraq's different communities and members of the government over the next two days.

Kouchner's visit came amid talks between Iraq's political leaders to try to revive national reconciliation efforts and repair the fractured unity government.

Prime Minister Nuri al-Maliki is under growing pressure from Washington, which is frustrated by negligible political progress while its troops step up operations to quell sectarian violence.

Former French President Jacques Chirac and his then foreign minister Dominique de Villepin were at the forefront of international opposition to the U.S.-led war.

AHMADINEJAD VISIT?

Sarkozy, elected in May, has sought to improve relations, saying he wanted France to be a friend of the United States. He paid an informal visit to the Bush family estate during his U.S. holiday where they chatted over burgers and hotdogs.

A White House spokesman welcomed Kouchner's visit.

"This is one more example ... of a growing international desire to help Iraq become a stable and secure country," spokesman Gordon Johndroe said.

Kouchner's appointment after Sarkozy's election in May was seen as significant for relations with the United States and with Iraq where France has no troops but has kept an embassy.

He has been a leading advocate of "humanitarian intervention" -- the right to get involved in another country's affairs if human rights are being abused.

Kouchner, co-founder of the Nobel Peace Prize-winning aid group Medecins Sans Frontieres, is one of the few French politicians who backed military intervention in Iraq, saying he was against war but also against Saddam Hussein's regime.

His visit coincided with the fourth anniversary of a truck bomb attack on the United Nations headquarters in Baghdad that killed U.N. envoy Sergio Vieira de Mello, a friend of Kouchner whom he met while working in Kosovo.

Kouchner visited the site of the attack and laid a wreath in remembrance of those who were killed.

The president of neighbouring Iran, Mahmoud Ahmadinejad, has accepted an invitation to visit Iraq, Iran's foreign minister said on Sunday, a move unlikely to be welcomed by Washington.

Iranian Foreign Minister Manoucher Mottaki said Iraqi Prime Minister Maliki had invited Ahmadinejad after visiting Tehran this month, but said 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.

U.S. officials and military commanders have stepped up their accusations against Iran in recent weeks, accusing Iraq's neighbour of playing a spoiling role to influence a progress report on the war due to be presented to Congress next month.

U.S. intelligence reports indicate there are about 50 members of Iran's Revolutionary Guards training Shi'ite militias in how to use mortars and rockets in southern Iraq, a U.S. general said on Sunday.

In Tehran, Foreign Ministry spokesman Mohammad Ali Hosseini dismissed the accusation as "completely baseless". (Additional reporting by Anna Willard in Paris; Ross Colvin and Aseel Kami in Baghdad, Fredrik Dahl in Tehran and Tabassum Zakaria in Washington)

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