The stalemate marks the third time in four Ligue 1 games that OM have failed to find the target and leaves them nursing a run of just two wins in eight stretching back to January 26.
The points sees Marseille close to within six of leaders Paris St Germain, but that gap could grow when the capital club travel to St Etienne to play their game in hand on Sunday.
Marseille will also be looking anxiously over their shoulders after their latest below-par display, with St Etienne and Nice three points back as the race for the final Champions League berth hots up.
Ajaccio ended a three-game winless run with a home win over Lorient last time out, and tonight’s solid defensive display keeps them in 13th, six points clear of relegation danger.
The hosts were the first to threaten at Stade Velodrome, 14 minutes on the watch when Andre Ayew released Modou Sougou but his volley from 20 yards was blocked by Guillermo Ochoa.
Two minutes later the hosts were on the front foot again, Ayew unleashing an effort after being found by Mathieu Valbuena although Ochoa was again up to the task.
OM goalkeeper Steve Mandanda was in action in the 20th minute to deny Frederic Sammaritano after good approach play by Adrian Mutu, while the Romanian striker was again the focus of the Ajaccio attack in the 36th minute when he teed up Johan Cavalli for a low drive that went inches wide.
Sammaritano fired into the side-netting as Ajaccio threatened early in the second half, but Marseille carved out the remaining chances in the match.
First Valbuena picked out Andre Pierre Gignac but his drive skimmed the woodwork on its way out.
With 63 minutes gone Joey Barton played in Sougou but Ochoa again came to the rescue, while the last chance to break the deadlock arrived with six minutes remaining as Rod Fanni crossed for Ayew but his header sailed over the bar.