It was supposed to be the first U.S.-Iranian exchange under the Obama administration.

Iran invited eight members of the U.S. women’s badminton team to play in an international tournament that started Friday, and the Iranian team was to visit the United States in July. The Americans were told to pick up their visas in Dubai, but when they arrived, the visas were denied.

Welcome to the internal Iranian debate over how to respond to President Obama’s overtures toward Tehran.

Barack Obama campaigned on a pledge to talk with Iran without preconditions — on issues ranging from Tehran’s suspect nuclear energy program to Iraq and Afghanistan. That distinguished him from the Bush team, which insisted that Iran halt its enrichment of uranium before any broad dialogue could begin.

In a recent interview with the Arab television station al-Arabiya, Obama said that “if countries like Iran are willing to unclench their fist, they will find an extended hand from us.”

Top Iranian leaders have been grappling with how to handle Obama’s offer. It confronts them with an unnerving challenge. Rather than encourage more U.S.-Iranian contacts, the Iranian government seems to be moving into reverse.

In December, a prominent American academic taking part in an exchange was detained in Iran and interrogated for hours, leading the National Academies of Science to suspend educational exchanges with Iran. Two Iranian brothers who worked with U.S. scientists on combating HIV/AIDS in Iran have been accused of spying.

Clearly, Iranian officials are dubious about whether Obama has really abandoned the Bush administration’s goal of Iran regime change. Equally important, the Islamic republic finds it hard to reverse a central ideological tenet of the past 30 years — anti-Americanism.

“It is a moment of truth for Iran,” says Karim Sadjadpour, a leading Iran expert at the Carnegie Endowment for International Peace. “For the last eight years it was possible to paint the United States as the aggressor. With Obama it will be much more difficult.”

Sadjadpour believes Iran’s current leaders “thrive when Iran has an adversary relationship” with America, which provides a distraction from the deteriorating economy. These leaders “recognize it is not to their benefit to open up to the United States.”

Certainly, the signals coming out of Tehran have been contradictory. Right after Obama’s election, President Mahmoud Ahmadinejad sent the president a congratulatory letter — the first such letter sent since Iran’s revolution.

But Ahmadinejad has made clear that Iran has its own preconditions for a thaw, even if Obama drops America’s. “Change has to be fundamental,” the Iranian president said last week. He says that includes dropping U.S. objections to Iran’s nuclear program, withdrawing all of its troops from abroad, and ceasing to support Israel.

Iran’s Ayatollah Ali Khamenei, who is the ultimate authority in the country, has been talking in equally harsh language. In a sermon on Dec. 8, he said Iran “neither wants America’s incentives nor its punishment.”

And I got a personal glimpse of how tough it will be for the Obama team to negotiate with the Iranians when I spoke with a top adviser to Ahmadinejad at the Davos World Economic Forum. Seyed Mojtaba Samare Hashemi Shajareh, a slight man with stubble beard and a button-down shirt but no tie, spoke in language that was frustratingly opaque. Still, he left no doubt that the Iranians want to play hardball.

“There should be some signals that … talks will go on and with mutual respect,” Seyed Hashemi insisted. “The last (Bush) administration occupied Iraq and had an aggressive policy. If … those aggressive policies are changed … we would be ready to talk. But will change be real, in aims and goals?”

He insists the United States must recognize Iran’s right to enrich uranium and produce fuel for nuclear plants.

No doubt Iran’s leaders are trying to position themselves for a formal Obama overture. They must also be thinking about Iran’s June elections, in which Mohammad Khatami, a popular and more moderate former president, may be competing against Ahmadinejad.

The upshot: Expect Iran to test Obama, or even try to discourage his efforts. Yet Obama should continue genuine efforts at dialogue.

He should propose direct talks not just on the nuclear issue, but in areas where U.S.-Iranian cooperation is vital — such as Iraq and Afghanistan. He should offer more U.S. visas for Iranian experts and students.

I agree with Sadjadpour, who says: “Don’t let spoilers set the tenor. Continue to express the desire for a change in the relationship. This will really put the pressure on Khamenei.”

The world will be waiting to see whether Iran dares accept Obama’s offer, or not.