Despite a swirl of rumors, the oil tanker Afrodite is still waiting in the Mediterranean, and the American University Hospital is still waiting for its shipment of fuel. And time is running out.

Dr. Nadim Cortas, dean of the medical center, says that for now the hospital is still operating, but only because two days ago Lebanon's electricity provider put all hospitals on a priority list to receive power. 

But, says Cortas, "It all depends on how much reserves the government has to get to the electricity company. We start to fail when they fail." And without government electricity, Cortas says, the hospital only has reserves to last "seven to 10 days."

The captain of the Afrodite and the ship's owner Tsakos Energy Navigation, the subsidiary of a Greek-owned company listed on the New York Stock Exchange, has said the ship wouldn't proceed through the blockade without a written guarantee of safe passage from the Israeli Defense Forces (IDF). When ABC News asked a Tsakos representative what is causing the hold-up, he refused to comment.

According to one American University administrator, U.S. State Department officials told him that the IDF is prepared to provide Afrodite with a written guarantee of safety and that the U.S. Navy is willing to escort the tanker. Neither the Israeli Embassy nor the U.S. State Department has confirmed the story, despite repeated requests from ABC News.

The World Health Organization warned yesterday that "if fuel is not delivered this week, 60 percent of all hospitals in Lebanon will cease to function."

Read ABC News' full coverage on Beirut hospital out of gas.