"Despite a night of worry and some scare tactics by the [Israeli] navy, we have landed in Egypt and are ready to make our way to help the people of Gaza," one of the flotilla activists told Egyptian news Web site Bikya Masr.
The ship was heading directly to Gaza when its steering apparently failed.
"The ship's aqua pilot sailing system has broken down and our ship is spinning, going in circles, and turning round and round. We are therefore unable to get out of the Egyptian territorial waters," a statement from the organization said.
On May 16, the boat was only 400 yards away from land when it came under fire from the Israeli navy, forcing it to retreat and seek anchorage, the group claimed.
The flotilla missions are an attempt to break the economic blockade on the Gaza Strip.