The Suez Canal Authority reportedly said that tug boats helped partially to refloat the container ship.
Two senior Egyptian marine sources said some traffic would be diverted but it was unclear that this could free up congestion, according to Reuters.
Canal authorities could not be immediately reached by the AP early Wednesday.
On a daily basis, about 600,000 barrels of crude or less flow from the Middle East to Europe and the US via the canal, while volumes from the Atlantic Basin to Asia total about 850,000 barrels a day, according to Anoop Singh, head of East of Suez tanker research at Braemar ACM Shipbroking Pte.
The ship is owned by container shipping company Evergreen Line.
Bloomberg reported it had caused a build-up of more than 100 ships seeking to transit the canal.
In 2015, Egypt's government opened a major expansion of the canal that deepened the main waterway and provided ships with a 35km (22 mile) channel parallel to it. The Ever Given was built in 2018 and stands 400m long and 59m wide.
"All crew are safe and accounted for", said Bernhard Schulte Shipmanagement, which manages the Ever Given.
The Ever Given attempted to pass through the canal while en route to Rotterdam, Netherlands but ran aground at about 6:00am Tuesday, local time, according to a report from maritime website Fleet Mon.
"This will take approximately one week more than the Suez routing - and also burn more fuel".
Bow Of The Ever Given.
Container shipping supply chains have faced a tough few months with port congestion and container shortages causing delays and driving up prices.
During 2020, almost 19,000 ships, or an average of 51.5 ships per day, with a net tonnage of 1.17 billion tonnes passed through the canal, according to the SCA.
According to tweets, tankers and container ships were stacking up at both ends of the canal as well as in Great Bitter Lake in Egypt.
"It increases the risk that we might see additional port congestion in European ports in the next week", said Lars Jensen, chief executive at SeaIntelligence Consulting.
Oil and gas flows will be affected majorly if the path is not cleared soon.
"This is the largest vessel ever to go aground in the Suez Canal", he said, adding that the ship got lodged in the embankment and would have lost power and its ability to steer.
The canal is a main source of foreign currency for Egypt, bringing in $5.6 billion in revenues in 2020. The ship ran aground some 6 kilometres (3.7 miles) north of the southernly mouth of the canal near the city of Suez, an area of the canal that's a single lane.
Shoei Kisen Kaisha Ltd., based in Japan's Ehime Prefecture, confirmed Wednesday that it was the owner of the Ever Given.
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