ROME — The Italian energy company Eni S.p.A. announced on Sunday that it has discovered a “supergiant” natural gas field off the coast of Egypt, describing it as the “largest ever” found in the Mediterranean Sea.

Eni’s chief executive, Claudio Descalzi, met on Saturday in Cairo with President Abdel Fattah el-Sisi of Egypt, according to Mr. Sisi’s office.

Eni said the discovery, made in its Zohr prospect “in the deep waters of Egypt,” could hold a potential 30 trillion cubic feet of gas over an area of about 40 square miles.

The discovery well is about 120 miles from the Egyptian coast, at a depth of 4,757 feet, in the Shorouk block, the company said. The block is about 66 miles from Port Said.