Several Americans who were held said they recognised Ahmadinejad as a ringleader. But two Iranians who were leading figures in the storming of the embassy said he did not take part.
Bush on Thursday said he did not know whether Ahmadinejad was involved and officials were analysing photographs and other information in what they said was a government-wide effort to get answers.
"Obviously his involvement raises many questions, and knowing how active people are at finding answers to questions, I'm confident they will be found," Bush told reporters.
Bush warned Ahmadinejad that he and European leaders would take a unified stance in their concerns over Iran's nuclear ambitions.
The US president has said little until now about Ahmadinejad, the 48-year-old former Tehran mayor taking over from reformist President Mohammed Khatami.
Ahmadinejad has struck a defiant stance on Iran's nuclear fuel programme and has dismissed calls for efforts to improve Iran's relationship to the United States.
Involvement by the new Iranian leader in the 1979-1981 hostage crisis would send a chill through the US government, which has not resumed diplomatic relations with Iran. Fifty-two Americans were held for 444 days.
"We have not forgotten"
US State Department spokesman
"We have not forgotten," State Department spokesman Sean McCormack said. He added that the Iranian government had a responsibility "to speak definitively concerning these questions that have been raised in public by these stories".
Retired Navy Captain Donald Sharer and Bill Daugherty said they were convinced Ahmadinejad was one of their Iranian captors.
"He wasn't a very nice fellow at the time. He called us pigs and dogs. He's very hardline; he's a guy we are not going to get along with," Sharer told ABC's Good Morning America.
Daugherty said he had "no doubts at all" that Ahmadinejad was one of his captors.
"When your country is being humiliated and being embarrassed, the individuals that do that really stick in your mind. You don't forget people who do things like that to you and your family and your country," Daugherty said.
In an interview on MSNBC, Sharer said he recognised Ahmadinejad from a recent picture printed this week in a newspaper.
"I'm 99% sure that the picture I looked at Tuesday was one of my captors," he said.
Some ex-hostages are convinced
Ahmadinejad was a captor
But Sharer said he did not believe that a man seen in a widely circulated photograph taken during the hostage crisis is Iran's new leader.
One US official who spoke on condition of anonymity said Ahmadinejad seemed to have moved "through the same circle" as the hostage-takers but added, "Was he a hostage-taker? That's the open question."
White House National Security Adviser Stephen Hadley said no determination had been made on photographs that some hostages believe show Ahmadinejad taking part in the siege.
In Iran, Abbas Abdi, who helped to orchestrate the raid, said Ahmadinejad "was not among those who occupied the American Embassy after the revolution".
Mohsen Mirdamadi, another ringleader, said reports of Ahmadinejad's role were untrue.
Bush, who in 2002 branded Iran as part of an "axis of evil", said he is speaking to the leaders of Britain, Germany and France about his concerns over Iran's nuclear programme.