"Egypt agreed to allow two Iranian warships to transit the Suez Canal," the official MENA news agency reported.
Canal officials say it would be the first time Iranian warships have made the passage since the 1979 Islamic revolution.
MENA reported that the request for the ship to pass said they were not carrying weapons or nuclear and chemical materials.
It is not known when the ships are expected to arrive at Port Said, the northern terminus of the canal on the Mediterranean. From there they are expected to sail to Syria.
Israeli Defence Minister Ehud Barak has labelled the Iranian action as "hostile' and said Israel was closely monitoring the situation.
Foreign Minister Avigdor Lieberman said an Iranian naval presence in the area was a "provocation that proves the self-confidence and cheek of the Iranians is growing from day to day".
Asked by AFP in Jerusalem to comment on the latest development, foreign ministry spokesman Yigal Palmor recalled Lieberman's comments on Wednesday.
"We have nothing to add to the minister's statement," Palmor said on Friday. "It's still valid."
Earlier, an Egyptian foreign ministry official said the Iranian request was passed on to the defence ministry, which has to approve the passage of any warship through the canal.
His comments came a day after a canal official and a shipping agent said the request had been cancelled, at the prompting of the Egyptian government. An Iranian diplomat said administrative reasons where behind the delay.
Iran's official Fars new agency, quoting senior naval commanders, has said the ships are the 33,000-tonne refuelling and support vessel Kharg and the 1,500-tonne light patrol frigate Alvand, both British-built.
The Kharg has a crew of 250 and can carry up to three helicopters. The Alvand is armed with torpedoes and anti-ship missiles