Morsi was quoted by the agency, which has ties to Iran's Revolutionary Guard, as saying he hopes to build the relationship between the two countries, Bikya Masr reported. Fars said it was told that would create a "strategic balance in the region."
Fars said it interviewed Morsi on Sunday before the results of the presidential election were announced. It has released an alleged recording of the interview, but reports in Egypt say the voice does not match Morsi's.
Morsi was a member of the Muslim Brotherhood, although he has since resigned. He said after his victory was announced that he would respect treaties Egypt has signed, although he did not mention the Camp David Accords in 1979 that recognized Israel.