State Department spokesman Adam Ereli suggested the Iran’s Friday decision reflected the extremely difficult conditions in Bam after the 26 December earthquake, which killed more than 30,000 people and left tens of thousands homeless.
"We have heard back today from the Iranians that given the current situation in Bam and all that is going on there now, it would be preferable to hold such a visit in abeyance. Therefore we are not pursuing it further at the moment," Ereli said.
It was unclear whether Iran's decision not to accept the visit reflected a calculated refusal.
Ereli declined to say whether a visit by Dole, a North Carolina Republican and former head of the American Red Cross, might take place at some point in the future and he stressed the United States would keep providing humanitarian aid to Iran.
The United States said its offer to send Dole, was a humanitarian rather than a political gesture.
One State Department official said: "The purpose of this visit was to send a positive signal; it was to be a positive signal of our concern for them. And if they're not comfortable with it, then it doesn't make sense to do it."
Iranian Foreign Ministry spokesman Hamid Reza Asefi was quoted by Iran's state television as saying, "Offering relief to survivors of the earthquake must continue without turning into a political issue because it's a humanitarian issue."
Washington cut ties with Tehran in 1980 after the Iranian revolution brought to power an anti-American government. The decision to sever ties was taken during the 1979-81 hostage crisis when Iranian students held 52 Americans for 444 days.