Most of the charges focus on Tehran's alleged financial support of southern Shi'a parties in the 30 January vote. Other charges allege that Iran has sent some 1 million citizens into southern Iraq to fraudulently cast ballots.
The accusations -- denied by Iran -- are hard to prove.
But some are widely taken to be at least partly true because Iraq's leading Shi'a religious parties were until recently in exile in Iran. The parties -- the Supreme Council for the Islamic Revolution in Iraq (SCIRI) and the Islamic Da'wah Party in Iraq -- opposed Saddam Hussein and waged a guerilla struggle against his regime from across the border.
Now, as the vote looks likely to produce a Shi'a majority in Iraq's new National Assembly, these parties are poised to become power brokers. The National Assembly will select Iraq's next government and oversee the writing of its new constitution even as the country remains secured by U.S.-led forces.
William Samii, a regional expert with RFE/RL in Washington, says the Shi'a religious parties' progress can only please Tehran. He calls it a first victory for an Iranian foreign policy that opposed the U.S.-British invasion of Iraq in 2003.
Samii says Iran has pursued two goals: securing its political interests in Baghdad and helping insurgents trying to evict U.S. troops by force.
"Then you saw actually a duality representing the splits within the Iranian government. You had the executive branch and Foreign Ministry basically recognizing the interim government in Iraq and trying to have regular business ties between the two countries. The other side was where you had elements within the Iranian government supporting the insurgents [and] making repeated comments about how the U.S. is getting stuck in a quagmire in Iraq," Samii says.
Samii says these dual policies at times appear contradictory because the key political parties in Iraq that Tehran supports participate in the U.S.-backed government fighting the insurgents. But while one policy aims at building future influence in Baghdad, the other addresses what Iran sees as the immediate threat of being encircled by U.S. forces.
Any humbling of U.S. troops by Iraq's insurgents could help persuade Washington to reverse military advances that, since 9/11, have included deploying forces in Iraq and Afghanistan and establishing bases in Central Asia.
But Samii says that if Iran is challenging the United States in Iraq to secure its regional interests, events in Iraq also pose challenges to the Iranian regime itself.
One is that strong Shi'a voter turnout will help speed the creation of a republican form of government next door that sharply contrasts with Iran's own theocratic system.
"You are not going to have a theocracy in Iraq, regardless of the outcome of the election. I just don't think the other competing parties in Iraq will allow that even though they are in a minority. They want a regular republican system of government. So, if you've got that right next to Iran, people are going to question why they have to have a theocratic government whereas the Iraqis are able to have a Shi'a-dominated but republican form of government," Samii says.
The U.S. daily "The New York Times" on 21 January quoted a senior member of the Islamic Da'wah Party as saying that Shi'a political leaders want the new Iraqi government to be secular. Adnan Ali told the paper: "There will be no turbans [clerics] in the government. Everyone agrees on that."
Another challenge for the Iranian regime is that any political success of Iraqi Shi'as could lead to a revival of the holy city of Al-Najaf -- in southern Iraq -- as the pre-eminent center of learning in the Shi'a world.
Under Hussein, the Iraqi Shi'a religious establishment was suppressed as a potential rival for power and Al-Najaf was partly eclipsed in the Shi'a world by the Iranian religious city of Qom. Respect for Qom has translated into credibility for Iran's clerical leadership, which is based there and espouses the principle of theocratic government.
Some analysts predict that a renaissance for Al-Najaf could weaken the Iranian theocracy by directing Shi'a attention to the alternative principles espoused by the Iraqi Shi'a religious establishment instead. Its leadership favors clerics guiding the faithful but staying out of politics.
Ammar al-Shahbander, a regional expert with the Institute of War and Peace Reporting in London, says any resurgence of Al-Najaf at the expense of Qom could have a profound impact not only inside Iran but across the Middle East.
"A strong Shi'a government in Iraq means that Al-Najaf will regain its power and will start influencing Shi'a groups around the world. The first place that is going to be affected is Lebanon, and that does not suit the Iranian and Syrian interests," Al-Shahbander says.
Iran and Syria are major benefactors of the Lebanese-Shi'a Hizbollah, which drove Israel out of southern Lebanon in 2000. The victory was welcomed by Tehran -- which does not recognize Israel -- and Damascus, which wants back the Israeli-held Golan Heights.
Beyond the Mideast conflict, al-Shahbander says a revival for Al-Najaf could give Shi'a minorities in many countries a renewed sense of pride after decades of marginalization by Sunni-dominated Arab governments. Substantial Shi'a miniorities exist in Saudi Arabia and Bahrain, while smaller communities can be found across the Arab world.
"For the past 20 years they have been able to [marginalize] these small Shi'a communities by claiming that they follow Iran, and by [accusing the Shi'a of] following a foreign, non-Arab country, that gave these governments the right to exclude them from any political process. But now, Iraq is an Arab country, and if the Shi'a communities around the Arab world start to look up to Iraq, rather than to Iran, it means that they become a real part of their own countries and they will claim the right to participate," al-Shahbander says.
Many governments in the region have said they support holding elections in Iraq on 30 January. But they have also expressed concern over the extent to which Arab Sunnis will be represented in the vote.
Some community leaders in Sunni areas of central Iraq -- where insurgents are most active -- have called for boycotting the polls over poor security or because they fear the poll will hand power to the Shi'a majority.