Photo: Suhaib Salem / Reuters
Diplomatic relations between the two countries have been severed for more than 30 years, but both sides have signalled a shift in policy since former president Hosni Mubarak was overthrown last year in a popular uprising.
Fars quoted him as saying he was interested in better relations with Tehran. "This will create a balance of pressure in the region, and this is part of my program."
Asked to comment on reports that, if elected, his first state visit would be to Iran's regional arch-rival Saudi Arabia, Morsy said: "I didn't say such a thing and until now my first international visits following my victory in the elections have not been determined".
Fars said he was speaking a few hours before the results of the Egyptian election were announced on Sunday.
Morsy's comments on Iran came just prior to his first speech since his election win, during which he vowed to "preserve international accords and obligations," in what appeared to be a reference to the peace treaty with Israel.
Morsy attempted to allay fears that he would immediately act to Islamize Egypt, promising to be a president to all Egyptians, "Muslims, Christians, the elderly, children, women, men, farmers, teachers, workers, those who work in the private and public sectors, and the merchants."
The new Egyptian president thanked the "martyrs" that had lost their lives during the uprising that led to the ouster of former president Hosni Mubarak, saying the he would not have become president without their sacrifice.
Morsy did not call out a challenge to Egypt's military leaders for their recent attempts to limit presidential powers, instead praising the army and police as "brothers."
Morsy defeated former Mubarak prime minister and general Ahmed Shafik in a run-off last weekend by a convincing 3.5 percentage points, or nearly 900,000 votes, taking 51.7 percent of the total, officials said. It ended a week of disputes over the count that had frayed nerves.
Morsy succeeds Mubarak, who was pushed aside by his fellow officers 16 months ago to appease the Arab Spring revolution.
The military council which has ruled the biggest Arab nation since then, curbed the powers of the presidency by decree last week, meaning the head of state will have to work closely with the army on a planned democratic constitution.
The generals say they want to hand over to civilian rule but are plainly set on defending their privileges and suspicious of the ability of Egypt's fragmented, and long oppressed, political movements to establish a stable constitutional democracy.
Obama calls to congratulate Morsy on victory
US President Barack Obama called Morsy on Sunday to congratulate him on his victory. According to a White House statement, Obama underscored that the US will continue to support Egypt’s transition to democracy and stand by the Egyptian people as they fulfill the promise of their revolution. He emphasized his interest in working together with Morsy, on the basis of mutual respect, to advance the many shared interests between Egypt and the United States.
Morsy welcomed Obama's support and the two leaders affirmed their commitment to advancing the US-Egypt partnership and agreed to stay in close touch in the weeks and months ahead, according to the statement.
Obama also called Shafik, commending him on a well-run campaign, according to the US State Department.
Reuters contributed to this report.