Canal officials said some progress had been made, however, and more tugboats were joining the effort on Sunday.
Alternative arrangements are being put in place in case the operation fails.
Egypt's President Abdul Fattah al-Sisi has ordered preparations to lighten the load of the stranded ship.
That would involve transferring some containers to another vessel or to the canal bank. Experts earlier told the BBC that such an operation would involve bringing in specialist equipment, including a crane that would need to stretch more than 60m (200ft) high, and could take weeks.
The Suez Canal is one of the world's busiest trade routes, and the Ever Given - part of the Evergreen fleet - has been wedged in it since Tuesday.
More than 300 ships are stuck on either side of the blockage and some vessels have had to reroute around Africa.
On Saturday 14 tugboats pulled and pushed the Ever Given at high tide to try to dislodge it. At the same time, dredgers continued to remove thousands of tonnes of sand and clay from where the bow was trapped in the canal's bank.
Although strong tides and winds complicated efforts, the tugboats managed to move the ship "30 degrees from left and right", said General Osama Rabie, chairman of the Suez Canal Authority (SCA).
Footage posted on Twitter appeared to show the tugboats honking their horns to celebrate this small victory.
The SCA said in a statement that dredgers had so far shifted 27,000 cubic metres of sand to a depth of 18m (59ft).
Gen Rabie said on Sunday that although the vessel was still stuck there were "positive indicators" from the past two days' efforts.
"The rudder was not moving and it is now moving, the propeller is working now, there was no water underneath the bow, and now there is water under it, and yesterday there was a 4m (13ft) deviation in the bow and the stern," he told Egyptian state TV.