Mr Ghobadi said he was worried about Ms Saberi's health and depressed state.
He also asked to be allowed to testify at her appeal, saying that "she is innocent and guiltless" of the charges.
Ms Saberi was tried and sentenced behind close doors last week by the Revolutionary Court in Tehran. She was jailed for eight years on charges of being an American spy.
Her father says her appeal against the sentence could be heard as early as next week.
During the ABC News interview, President Ahmadinejad was asked whether he would free Ms Saberi as a humanitarian goodwill gesture, following US President Barack Obama's recent personal assurance that she was not a spy.
But the Iranian president stressed that it was up to the courts to decide what to do.
"I am not a judge, and I do not pass judgment over judicial cases," President Ahmadinejad said, in the interview with ABC News' George Stephanopoulos.
"In Iran, the judiciary is independent. I have stressed like others she should be accorded her full rights."
President Ahmadinejad was also non-committal when his interviewer asked to be allowed to see Roxana Saberi for himself to check that she was safe.
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