Officials with the authority told reporters that further tugging operations would resume to fully restore the ship in the right direction once the tide rises later Monday.
The 400-meter ship became jammed diagonally across a southern section of the canal in high winds on March 23, halting shipping traffic on the shortest shipping route between Europe and Asia.
While the canal is still not open, Egyptian President Abdel Fattah al-Sisi from his official Twitter account wasted no time declaring the crisis over.
“By restoring matters to their normal course, with Egyptian hands, the whole world will be assured of the path of its goods and needs that are passed by this axial navigational artery,” he tweeted.
But the CEO of the salvage company involved in the rescue efforts told Dutch public radio the operation was far from complete.
The developments come after nearly a week of blocked traffic at the key shipping route connecting the Red Sea to the Mediterranean Sea.
More than 360 ships were waiting to enter the canal as of late Sunday.
Egypt is eager to resume traffic along the Suez Canal, which brings in between $5 billion and $6 billion in revenue each year. According to a study by German insurer Allianz, each day of the blockage in the canal could cost global trade between $6 billion and $10 billion.
Some maritime firms responded to the delays by deciding to divert ships around the Cape of Good Hope, at the southern tip of the African continent.
After further dredging and excavation over the weekend, efforts by rescue workers from the SCA and a team from Dutch firm Smit Salvage worked to free the ship using tug boats in the early hours of Monday, two marine and shipping sources said.
Marine traffic through the canal will resume once the ship is directed to the Great Lakes area, a wider section of the canal, it added. As of early Monday, at least 369 vessels were waiting to transit the canal.