By Samia Nakhoul and Parisa Hafezi

TEHRAN, Jan 21 (Reuters) - Iraqi factions are heeding Iran's advice to halt violence but the best solution to Iraq's problems would be for the United States to withdraw its troops, an aide to the Iranian president said on Monday.

U.S. and Iranian officials held several rounds of rare face-to-face talks in Baghdad to find ways of ending sectarian bloodshed and an insurgency that has brought thousands of deaths of Iraqis and U.S. troops since the 2003 U.S.-led invasion.

Washington and Baghdad, who say Tehran has stoked the violence by arming and training Shi'ite Muslim militias, say there has been a drop in attacks using Iranian-made weapons over the past few months, although they say training has continued.

Iran denies the charges and blames the conflict on the U.S. occupation, which it says ought to be brought to a swift end.

"We believe that all the (Iraqi) parties are moving toward greater calm in Iraq. They are listening to advice including from us," Aliakbar Javanfekr told Reuters at the compound for Iranian President Mahmoud Ahmadinejad in central Tehran.

"Americans could not get any result from their adopted policies ... Around 4,000 American soldiers were killed in Iraq (and with) the continuation of the occupation that number will increase and more corpses will go back to Washington."

"It is better for the United States to adopt a wise policy towards Iraq. We think the best policy for them is to withdraw from Iraq," he added.

Some Iraqi officials say the U.S. military presence is still needed while Iraqi forces manage to get control of the security situation in the country and on its borders.

Javanfekr said Washington should hand over control of government and security affairs to the Iraqis.

"We believe they (Americans) should let the Iraqi nation decide for itself and decide on its fate. Surely the Iraqi government has the ability to defend its borders," he added.

While Iran was committed to engaging with the United States on stabilising Iraq, it was not interested for now in expanding ties and normalising relations, Javanfekr said.

The two countries have not had diplomatic ties since 1980 and are locked in a row over Iran's nuclear ambitions, which Tehran insists is peaceful but Washington fears is ultimately aimed at building nuclear warheads.

"We have never refused talks over Iraqi national interests with the United States. But regarding bilateral talks, for the time being we don't think those ties are in Iran's interest."

He repeated Iran's position that Washington must first change its hostile approach towards Tehran.

"The United States should abandon its hegemonic behaviour regarding Iran. If they adopt a policy based on mutual respect, then we can think about resumption of ties," Javanfekr said.

U.S. President George W. Bush has said Iran remains a threat to world security even though a U.S. intelligence report in December said Iran had halted a nuclear weapons programme in 2003. Tehran denies ever having had such a plan.

Tensions flared again earlier this month when Washington accused Iranian boats of threatening their warships in the Strait of Hormuz waterway. Iran says the encounter was routine. (Writing by Edmund Blair; Editing by Richard Balmforth)

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