TEHRAN, Iran, AP -Iraq”s constitutional referendum Saturday is being watched closely in this country, where Shiite Muslims have long held power and have close ties with the Shiites now controlling their neighbor.

Publicly at least, the Islamic government here says it is neutral — and just looking for a democratic and peaceful outcome.

&#34We hope … a high majority of the Iraqi people will participate in the vote. Whatever the vote of the Iraqi people, the Islamic Republic of Iran will respect it,&#34 Foreign Ministry spokesman Hamid Reza Asefi said this week.

Relations between Iraq and Iran are among the most complex and contradictory in the Middle East. Each has traditionally viewed the other with a mixture of suspicion but also rarely spoken admiration.

For Iran, the biggest obstacle to any genuine friendship was always Iraqi leader Saddam Hussein, who launched a 1980 war against Iran that lasted nearly a decade.

That means Iran has benefited greatly from the U.S.-led invasion that toppled Saddam, even though it opposes the American presence and is leery of having the U.S. military on its doorstep. Thus, Washington handed archenemy Iran a precious gift by removing Saddam, the biggest regional threat to Iranians.

The war also paved the way for the rise to power of Iraq”s Shiite Muslim majority, the best scenario that predominantly Shiite Iran could have expected.

&#34Iran wants an Iraq that will not pose threats to it. Tehran doesn”t want to suffer more from Iraq,&#34 said Davoud Hermidas Bavand, a prominent Iranian political analyst.

There is little question that Iran hopes the referendum on the Iraqi constitution will help consolidate the power of Shiites in Iraq after decades of Sunni Arab domination.

Others see more sinister goals.

U.S. officials have accused Iran of secretly backing the Sunni-led insurgency in Iraq to reduce the impact of America”s victory there as it tries to strengthen democracy in the region. Tehran has repeatedly said it doesn”t see Iraq as a battleground between Iran and the United States.

British Prime Minister Tony Blair recently charged that new bombs used by insurgents in southern Iraq against British soldiers &#34lead us either to Iranian elements or to Hezbollah,&#34 the Iranian-backed militant group in Lebanon. Iran denies that, accusing the British government of making up the charges to cover up its failure to provide security in Iraq.

Arab nations, which are mostly Sunni Muslim and traditionally suspicious of Iran, have publicly accused Iran in recent weeks of trying to dominate Iraq and sending money and men to sway things in Iran”s favor. Iran also denied those charges.

There is no question that Iran has at least some emotional hold on many key Iraqi figures.

Prime Minister Ibrahim al-Jaafari lived in exile in Iran during Saddam”s rule, and President Jalal Talabani”s Kurdish party relied on covert Iranian support to shore up his position against both Saddam and Kurdish rivals.

Ayatollah Ruhollah Khomeini, the late founder of Iran”s Islamic Republic, received refuge from the shah”s police in the Iraqi holy city of Najaf.

But analysts say Iran”s influence in Iraq should not be overestimated.

&#34It”s totally wrong to say Iran has a big say in Iraqi affairs. Iraqi Shiites are Arabs more than they are Shiites,&#34 said Bavand, the Iranian analyst.

&#34Nobody should expect that Iraqi Shiites will always side with Persian Iran. And no one should expect to see an Iranian-style Shiite type of government be formed in Iraq,&#34 he added.

In the end, however, Iran seems certain to benefit from the new situation in Iraq. Besides bringing a government whose leaders have close ties with Iran, last January”s election also produced an Iraqi parliament dominated by Shiites.

Tehran University professor Sadeq Zibakalam said a democratically elected government in Iraq was the best choice for Iran.

&#34A majority of Iraq”s population are Shiites. So free elections obviously produce a Shiite-majority government, easing fears in Tehran,&#34 he said.