BAGHDAD, May 3 (Reuters) - Iran supports the Iraqi government in its fight against militants, the head of a delegation from Iraq's ruling Shi'ite alliance said on Saturday after returning from a visit to Tehran.

Deputy parliamentary speaker Khalid al-Attiya, reading a brief statement on Iraq's al-Furat television, said the delegation had "important and constructive" talks with Iranian officials about the security situation in Iraq.

Members of the United Iraqi Alliance had said the delegation was sent to Tehran to tell Iran to stop backing Shi'ite militias fighting U.S. and Iraqi security forces, underscoring Iraq's unease over the influence of its powerful neighbour.

But Attiya made no mention of the accusations.

"The delegation saw a positive stance from the brothers in Iran to support the government's efforts in extending the sovereignty of the state and to fight the outlaws," Attiya said.

"The delegation hopes this visit is the basis for strengthening relations between the two neighbouring states."

Members of the delegation, which included several influential officials including at least one close to Prime Minister Nuri al-Maliki, have not been reachable since they returned on Saturday from their trip, which lasted several days.

While the delegation was in Iran, members of the Alliance had said the team would present evidence that showed Iranian support for Shi'ite militias in Iraq.

Iraqi government spokesman Ali al-Dabbagh had said the delegation had taken questions to Tehran that needed answering.

Washington accuses Shi'ite Iran of arming, training and funding rogue elements of the Mehdi Army militia of anti-U.S. Shi'ite cleric Moqtada al-Sadr. Iran denies the charges.

The U.S. military said this week that "very, very significant" amounts of Iranian weaponry had been found in the southern city of Basra and also Baghdad during an offensive against militiamen in those cities that began in late March.

Some of those arms were made in 2008, the military says.

U.S. military officials had planned to put on display some of the recently captured weapons but decided to let the Iraqis make their own case to Iran first.

Iran and Iraq fought an eight-year war in the 1980s in which hundreds of thousands were killed. Ties have improved since Sunni Arab leader Saddam Hussein was ousted in the U.S.-led invasion and a Shi'ite-led government came to power in Baghdad. (Writing by Dean Yates; Editing by Charles Dick)

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