Philip Craven offered his sympathy to the family of Bahman Golbarnezhad on what he described as "an absolutely tragic day for the Paralympic movement".
Iranian Golbarnezhad died after suffering a cardiac arrest following a crash in the men's C4-5 road race on Saturday.
Speaking at a media conference, International Paralympic Committee president Craven said: "This an absolutely tragic day for the Paralympic movement and the Rio 2016 Games.
"It's changed the way I feel today. I can say to all the people of the Islamic Republic of Iran and particularly the family of Bahman Golbarnezhad, the International Paralympic Committee offers its deepest condolences."
Denying that budget cuts made before the start of the Games impacted the incident, Craven added: "There were no cuts that affected this. The ambulance that attended, attended within two minutes.
"It had all the latest equipment on it and there was a doctor and a nurse present. Everything that was done was in order to save Bahman's life."
Paying tribute to Golbarnezhad, secretary of the Iranian Paralympic Committee Masoud Ashrafi said: "We are disheartened and heavy with the news.
"Bahman was one of the most hard working and active athletes we've had.
"He has been cycling for 12 years and he's our best cyclist. He's married. He has a wife and one son.
"He was the kind of man who was a family man. He loved his family."