The 400-metre, 224,000-tonne Ever Given ran aground on Tuesday morning after losing the ability to steer amid high winds and a dust storm, the Suez Canal Authority (SCA) said in a statement.
About 30 per cent of global container shipping volumes pass through the canal each day, carrying everything from fuel to consumer goods.
The main alternative route for ships travelling between Asia and Europe, around the African cape, takes a week longer to navigate.
GAC, a Dubai-based marine services company, said authorities were still working to free the ship mid-afternoon on Wednesday and that information it had received earlier claiming the vessel was partially refloated was inaccurate.
Images posted by the SCA appeared to show the ship positioned diagonally across the canal, blocking its full width, as tugs tried to dislodge it. Photos showed a digger removing earth and rock from the bank of the canal around the ship's bow.
An official said work to release the ship could continue into the night, weather permitting.
The SCA's chairman told local media that despite the blockage, a southbound convoy was on the move and that the authority was trying to keep traffic flowing between waiting areas as best it could while salvage efforts continued.
"Once we get this boat out, then that's it, things will go back to normal. God willing, we'll be done today," Chairman Osama Rabie said.
The authority was considering compensation for delayed ships, he said.
About 12 per cent of world trade by volume passes through the canal and it is a major source of hard currency for Egypt.
Tracking maps had shown the ship grounded in the southernmost stretch of the waterway, between the Great Bitter Lake and the Red Sea port of Suez.
At least 30 ships were blocked to the north of the Ever Given and three to the south, local sources said. Several dozen ships could also be seen grouped around the northern and southern entrances to the canal.
The SCA said it was trying to rebalance the ship and local sources said efforts could shift towards digging the ship out if the tug boats were unable to release it.
Bernhard Schulte Shipmanagement (BSM), the ship's technical manager, said the Ever Given had run aground in the canal on Tuesday morning. BSM said the crew were safe and there were no reports of pollution.
A BSM spokesperson said the vessel was owned by Japan's Shoei Kisen KK, declining to provide further details. Shoei Kisen KK could not be reached for comment.
Taiwan's Evergreen Marine Corp, which is leasing the vessel, said the owner had told it the ship "was suspected of being hit by a sudden strong wind, causing the hull to deviate from (the) waterway and accidentally hit the bottom".
Dozens of ships carrying crude, liquefied natural gas (LNG) and retail goods were unable to sail through the canal on Wednesday, potentially disrupting supplies to global markets, shipping sources said.
Oil analytics firm Vortexa said 10 tankers carrying 13 million barrels of crude could be affected.
Oil prices rose more than 2 per cent on Wednesday.