Mr Bush urged Iran's unelected leaders to abandon what he termed their uncompromising, destructive policies which denied Iranians the opportunities and human rights of people elsewhere.
Prominent cleric Ayatollah Jalaluddin Taheri resigned on Tuesday, accusing the authorities of corruption and repression.
In response Iran's supreme leader, Ayatollah Ali Khamenei, said he agreed with some of the criticism, but warned that it would be used by Iran's enemies.
Several thousand people took to the streets of Tehran on Tuesday to mark the anniversary of violent street protests three years ago.
In a demonstration of dissatisfaction at the pace of reform in Iran, students clashed with plainclothes security officers.
In his written statement Mr Bush expressed solidarity with the students, saying, "their government should listen to their hopes."
"In the last two Iranian presidential elections and in nearly a dozen parliamentary and local elections, the vast majority of the Iranian people voted for political and economic reform," Mr Bush said.
"Yet their voices are not being listened to by the unelected people who are the real rulers of Iran," he added.
Change of tack
Mr Bush bemoaned the fact that students and professionals in Iran seek new lives abroad because of repression and economic disruption there.
In a statement that seemed in contrast to his State of the Union address in which Mr Bush listed Iran as part of an "axis of evil", the president said the US was Iran's ally.
"As Iran's people move towards a future defined by greater freedom, greater tolerance, they will have no better friend than the United States of America," he said.
Following Ayatollah Taheri's resignation on Wednesday, Ayatollah Khamenei tried to calm the situation by saying he agreed with some of the criticism levelled at Iran's leadership.
"I also have been saying for several years that we have to mobilise all possible means to fight poverty and corruption," Ayatollah Khamenei said.
But Ayatollah Khamenei, who is supported by powerful conservative clerics, warned that dissent among Iran's leaders would be seized upon by the country's enemies.