But to what extent does Europe share those concerns?
The answer is becoming clearer as EU leaders continue to react to last week’s Iranian poll.
EU foreign policy chief Javier Solana said yesterday he sees no reason to immediately change the EU's policies on Iran.
"The most important thing is to wait and see how the words are translated into actions. I have my doubts about some of the manners in which the elections have taken place, but in any case I want to wait and see the actions more than the words," Solana said.
Speaking in Brussels, Solana reminded Iran's new leadership that increased trade and economic ties would depend on progress on the nuclear issue and commitments on human rights and the Middle East.
Meanwhile, European Commission spokeswoman Emma Udwin has called on Tehran to swiftly and transparently investigate charges that last week's election runoff was riddled with irregularities.
Those charges were voiced for Europe by British Foreign Secretary Jack Straw. He said one day after the election that there was widespread interference by organs of the Iranian regime and undue limitations placed on the electoral process by Iran’s Guardians Council.
Udwin also underlined that the EU's Iran priorities won't change.
"There have throughout been four major priorities: there is the WMD [Weapons of Mass Destruction] issue, human rights, terrorism, the situation in the Middle East. Those remain our priorities in our dealings with Iran and that isn't changed by this change of personnel," Udwin said.
Germany, Britain, and France say they strongly hope Iran will continue negotiations with them that are aimed at convincing Iran to permanently give up sensitive uranium enrichment activities.
British Prime Minister Tony Blair, speaking in London yesterday, said the EU must not soften its approach, and called on Tehran to live up to its nuclear commitments.
Visiting Washington yesterday, German Chancellor Gerhard Schroeder said he agreed with U.S. President George W. Bush that the West must take a firm line with Iran.
"I couldn't agree more with [U.S. President George W. Bush's] message and we are going to continue being tough and firm on all of that. The message must stay very crystal clear, and it is. And second, the new president has emphasized that he wants the [nuclear] talks to continue, so here we are," Schroeder said.
Schroeder said the EU needs credible guarantees that Iran will not build atomic bombs.
In Warsaw, German Foreign Minister Joschka Fischer and his French counterpart Philipe Douste-Blazy urged Iran to keep a commitment it made to its European negotiating partners in November.
The commitment involved suspending uranium enrichment so long as the talks with Britain, France, and Germany continue. The three states are offering Iran trade incentives and help with its peaceful nuclear energy program if it agrees to give up activities that could lead either to producing nuclear fuel or producing material for nuclear bombs.
Mohammad-Reza Djalili is a professor at the Graduate Institute of International Studies in Geneva who has recently published a book titled “Geopolitics of Iran.”
He tells RFE/RL that the Europeans seem to acknowledge that Tehran’s position on major issues is not likely to change following the election of the president.
"The Europeans want to see acts, besides official declarations. And this can only happen when [Ahmadinejad] will enter his function in August. We feel that the Europeans are fully conscious that the main orientations regarding [Iran's] foreign policy do not only dependent on the Islamic Republic's president, that these orientations come from the supreme leader, that this supreme leader is staying in office, and that things are not going to change fundamentally," Djalili said.
Ahmadinejad on 26 June vowed that Iran would pursue peaceful nuclear development under his leadership.
He also said the nuclear talks with the Europeans were likely to continue, though with Iran's "national interest" in mind.
Besides, Ahmadinejad pledged to form a government of "moderation," saying Tehran would reach out to the international community.