The 400 m (430 yard) Ever Given, almost as long as the Empire State Building is high, is blocking transit in both directions through one of the world's busiest shipping channels for oil and grain and other trade linking Asia and Europe.
The Suez Canal Authority (SCA) said eight tugs were working to move the vessel, which got stuck diagonally across the single-lane southern stretch of the canal on Tuesday morning amid high winds and a dust storm.
"We can't exclude it might take weeks, depending on the situation," Peter Berdowski, CEO of Dutch company Boskalis which is trying to free the ship, told the Dutch television program "Nieuwsuur".
A total of 156 large container ships, tankers carrying oil and gas, and bulk vessels hauling grain have backed up at either end of the canal, Egypt's Leith Agencies said, creating one of the worst shipping jams seen for years.