Six more ships also arrived in the canal Sunday, bringing the total number of vessels stranded by the blockage to 327.
Lieutenant-General Osama Rabie, the chairman of the canal authority, "sent a message of reassurance to the global maritime community to resume navigation in the canal once the vessel is fully floated soon and directed to wait in the Lakes region for its technical examination", said the SCA statement.
The 1,312-foot, 200,000 metric ton Ever Given - almost a quarter-mile long - had created shipping nightmare and captured the public's imagination when it blocked the canal on Tuesday.
About 12% of global trade, around one million barrels of oil and roughly 8% of liquefied natural gas pass through the canal each day.
Egypt's Leth Agencies tweeted the ship had been partially refloated, pending official confirmation from the Suez Canal Authority (SCA).
The blockage has stopped traffic coming from both directions and forced companies to consider taking a more expensive route that diverts vessels past South Africa's Cape of Good Hope.
The blockade has lingered for nearly a week and has left hundreds of ships waiting on both sides of the canal which is a 200km shortcut from Asia to Europe, connecting the Red sea to the Meditteranean sea.
Stranded container ship Ever Given, one of the world's largest container ships, is seen after it ran aground, in Suez Canal March 25, 2021.
That translates to some 0.2 to 0.4 percentage points of annual trade each week.
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"Most major container lines are now diverting ships round Cape of Good Hope and warning of supply chain disruption ahead".
More than 320 ships are stalled at either end, Rabie said.
"It is a good sign", he said, adding that 14 tugboats were deployed around the stricken vessel and salvage crews were working round the clock.
About 27,000 cubic feet of sand have been removed from around the vessel to a depth of almost 60 feet.
The German radio, NDR, said that ongoing European discussions at the level of the European Union are demanding that EVER GIVEN ship should be prevented from passing through any port in Europe due to its repeated technical problems that affect global navigation and the failure of its captain to control it.
"Suppliers' delivery times have lengthened since the start of the year and are now longer in Europe than during the peak of the Covid-19 pandemic", it said.
Some 369 ships are now stalled as they wait for the canal to reopen, Rabie told the Al-Arabiya news channel Sunday.
Syria on Saturday announced it had begun to ration oil supplies including diesel and gasoline due to the blockage.
Numerous countries offered their assistance in the rescue operation, including the United States, China, Greece and the UAE.