In an interview with CNN, Rafsanjani said there has been small progress, but there was a lot of room for improvement in relations.
"Before the (1979 Islamic) revolution, you supported the regime of the shah that treated people very badly, and even after the revolution the United States has not been very good to us," he said.
U.S. President George Bush wants to increase international pressure on the country to halt what the administration believes to be a secret nuclear weapons program, which Rafsanjani said was being dealt with.
"We are going to give assurances that the (uranium) enrichment will not be for military purposes," Rafsanjani said.
Rafsanjani served two terms as Iran's president from 1989 to 1997, and is considered the favorite to win Friday's presidential election. His chief rivals are top reformist candidate Mostafa Moin and hard-liner Mohammad Baqer Qalibaf. President Mohammad Khatami is ineligible to run because of term limits.