TEHRAN, May 4 (Reuters) - Iran backs efforts by the Iraqi government to disarm militiamen, an Iranian news agency said on Sunday, after Baghdad said a delegation was sent to Tehran last week to urge it to stop supporting Shi'ite militias.

The delegation from Prime Minister Nuri al-Maliki's ruling United Iraqi Alliance (UIA) travelled to Iran after fresh U.S. accusations that Iranian-made weapons were found in Iraq.

Iran confirmed discussions took place with the visiting Iraqi delegation to help end fighting in its neighbour. Tehran has in the past denied supporting militias loyal to anti-American cleric Moqtada al-Sadr.

"We support the Iraqi government's efforts to disarm militiamen but we also advise (it) to avoid confronting people," ISNA news agency quoted an unnamed official as saying.

The official said Tehran would continue to support the Iraqi government and "make its utmost efforts to establish security in Iraq".

His comments were in line with those of the head of the Iraqi delegation, who said on Saturday after returning from Tehran that Iran supports the Iraqi government in its fight against militants.

Washington accuses Tehran of trying to destabilise Iraq by funding, training and providing weapons to Iraqi militias. Iran denies this and blames the U.S. troop presence for the violence.

Iran and Iraq, both mainly Shi'ite Muslim countries, fought a 1980-88 war that killed about one million people but relations have improved since the U.S.-led invasion in 2003 that toppled Saddam Hussein. Iran's influence in Iraq has also increased.

Maliki launched a crackdown on Sadr's militia in late March that met fierce resistance from well-armed fighters, and he says he is determined to disarm them.

An Iraqi security spokesman said last week that Iraq had seized Iranian-made missiles and heavy weapons in the last four weeks in the capital.

U.S. officials say they have collected proof of Iranian weapons that have arrived recently in Iraq, but were holding off making a public display of their evidence so that Iraqis could make their own case to Iran first.

Analysts say Tehran wants to keep a friendly, Shi'ite-led government in charge but wants to ensure rival Iraqi Shi'ite factions look to Iran as a power broker. They also say Iran wants to make sure U.S. troops do not get an easy ride in Iraq.

Tehran and Washington are also at loggerheads over Iran's disputed nuclear work, which the West fears is a disguised attempt to build atomic bombs. Iran says its plans are peaceful and aimed at generating electricity.

Washington has not ruled out military action against Iran if diplomacy fails. (Writing by Zahra Hosseinian; Editing by Myra MacDonald)

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