The call appeared to be the first contact between the two leaders since Mursi was sworn in as president of Egypt, a country which has not had diplomatic relations with Tehran for 30 years.
Ahmadinejad invited Mursi to attend a summit of the Non-Aligned Movement scheduled to be held in Tehran on Aug. 29, the state news agency said, quoting Mursi's spokesman. It did not say whether he had accepted.
Ties between Cairo and Tehran were severed in 1980 following Iran's Islamic revolution and Egypt's recognition of Israel.
Mursi has denied giving an interview to Iran's Fars news agency which had quoted him as voicing interest in restoring the long-severed ties between the countries. Mursi's spokesman said last week the interview never took place and that Mursi would file a lawsuit against the news agency.