CAIRO, Egypt (AP) _ Worldwide groups promised food and airlifted supplies Thursday into the Sudan, where torrential rains caused massive flooding that left 1.5 million people homeless and at least 11 dead.

In southern Egypt, rescue teams pulled 10 bodies out of the Nile River after a cruiser capsized and sunk during a storm a day earlier, the Middle East News Agency reported. They were identified as six Italian tourists and four Egyptians.

Ten Italian nationals and 13 Egyptians were missing, the state-owned news agency said.

Electric power was restored to parts of the Sudanese capital of Khartoum, but the country still faced the dangers of an overflowing Nile River and the possible outbreak of diseases.

In its early Friday edition, the state-run al-Ahram daily said 33 airplanes carrying food, medicine and relief supplies had arrived in Khartoum, including 20 from Egypt, seven from Saudi Arabia and others from Italy, Britain and Jordan.

In Rome, the World Food Program announced Thursday it was supplying more than 6,000 tons of emergency food aid to flood victims.

''The quantities, together with bilateral aid provided from locally available stocks, will be sufficient to feed ... about 1 million people'' for one month, the agency said in a statement.

The United States has arranged to airlift more than 850 rolls of plastic sheets to serve as tents for some of the homeless. It is also sending 1,200 tons of grain and food and $1 million worth of other relief supplies.

The Geneva-based International Red Cross said it was sending 2,000 tons of food. Red Cross offices in Britain, the Netherlands and Denmark are flying in 1,000 tents, nearly 50,000 blankets and 1 million water purification tablets.

National Red Cross societies and governments also have pledged $615,000 to purchase flour, cooking oil and other supplies.

The World Food Program said relief workers fear outbreaks of cholera, dysentery and malaria.

Sudanese officials blamed the recent floods on inadequate drainage systems. Last week's rainfall in Khartoum and its surrounding areas was 8.4 inches, compared with only 1.44 inches during all of 1987.

Khartoum and three other cities in eastern and northern Sudan have been declared disaster areas, and Prime Minister Sadek el-Mahdi has announced a nationwide state of emergency for six months.

The Blue Nile, which converges at Khartoum with the White Nile to form the Nile River, was rising rapidly behind the Sennar and Rosseire dams.

The possibility of the Nile overflowing its banks will be determined during the last 10 days of August, Sudan's Irrigation Minister Mahmoud Beshir said Thursday.

MENA said Thursday that the Blue Nile had covered 150 houses on the island of Tuti facing Khartoum, and the government was instructing inhabitants to place sand bags along the river bank to stop the rising waters.

The Nile has surged beyond levels recorded in 1946, when it had its worst flood on record, Khartoum's governor, Gen. El-Fateh Abdoon, was quoted by MENA as saying.

In Egypt, the steamer Nubia was sailing from Aswan to Luxor when it capsized and sank near the town of Edfu in a storm Wednesday. It was carrying 51 Italians and an Egyptian crew of 45.

An Italian Embassy spokesman in Cairo said 35 Italians were rescued, some suffering minor injuries and shock, on Wednesday. The spokesman, who spoke on condition of anonymity, said the remaining 16 Italians were missing, and Egyptian police said they were presumed dead.

Twenty-seven Egyptian crewmen also were rescued Wednesday and the body of one was picked up from the water. Thursday's recovery of the bodies of four Egyptians left 13 Egyptian crewmen missing.

Both Luxor and Aswan are favorite tourist resorts. Luxor is famed for its Valley of the Kings Pharaonic necropolis and the Karnak temple complex.