The Ever Given container ship has been anchored in a lake between two stretches of the canal since it was dislodged on March 29.
It had been grounded across the canal for six days, blocking hundreds of ships and disrupting global trade.
The Suez Canal Authority (SCA) demanded $916 million in compensation to cover salvage efforts, reputational damage and lost revenue, before publicly lowering the request to $550 million.
The Ever Given’s Japanese owners Shoei Kisen and its insurers have disputed the claim and the ship’s detention under an Egyptian court order.
Negotiations had been continuing until Saturday, SCA lawyer Khaled Abu Bakr told a court hearing in Ismailia over the ship’s detention.
The ship’s owners had put in a new offer, he said, without giving details.
The SCA’s chairman previously said Shoei Kisen had offered to pay $150 million.
A court ruling was due on Sunday after several delays, but Shoei Kisen’s legal team asked to allow more time for negotiations, one of their lawyers said.
Judicial sources said the case was postponed until July 4 to allow for “friendly settlement” between the parties.
This week UK Club, one of the ship’s insurers, said it was engaged in “serious and constructive negotiations” with the SCA, and was “hopeful of a positive resolution to these negotiations in the near future.”