During an interview with the Wall Street Journal, made public on Friday, the US president said he personally approved granting a visa to Iran's former president, Mohammad Khatami, who made several speeches in the US this week.
"I was interested to hear what he had to say," he said.
"I'm interested in learning more about the Iranian government, how they think, what people think within the government."
Despite the apparent change of tone, Bush repeated his view that Iran should not be allowed to acquire a nuclear weapon.
Khatami is the most prominent Iranian to visit the US since diplomatic relations were broken off in 1979.
"In order for diplomacy to work, it's important to hear voices other than current president Mahmoud Ahmadinejad's"
In a series of speeches delivered during the US tour, Khatami also sounded a conciliatory note, arguing that the two countries must stop trading threats and restart dialogue.
He also told reporters that a freeze on Iranian nuclear activities could be discussed during negotiations but that its suspension should not be a pre-condition to talks.Bush expressed the hope that Iranians will be persuaded to give up any ambitions they may have to acquire nuclear weapons through diplomatic means.
"And in order for diplomacy to work, it's important to hear voices other than current president Mahmoud Ahmadinejad's," he said.
The statement came just three days after Bush, in one of his speeches on the war on terror, compared leaders in Tehran to al-Qaeda terrorists.
On Thursday, the White House dismissed off-handedly an offer from Ahmadinejad to have a debate with Bush at the UN later this month, when the Iranian president is expected to be in New York to address the UN General Assembly.
Bush is scheduled to address the assembly on September 19.