The Dreamliner's reliability rate is now around 98 percent, meaning that two out of every 100 flights is delayed, above the 97 percent reported in October but still short of the firm's target, Fleming told a news conference in Oslo.
"I'll tell you that's not where we want the airplane to be, we're not satisfied with that reliability level of the airplane, the 777 today flies at 99.4 percent ... and that's the benchmark that the 787 needs to attain," Fleming said.
The Dreamliner was supposed to be a game-changer for the aviation industry as its lightweight body and sophisticated engines cut fuel consumption by 20 percent.
But it has been beset by problems, including a battery fire that grounded the model for three months last year and forced Boeing to redesign the battery.
Norwegian Air, the only European budget carrier to fly long haul, has been especially badly hit after a long string of breakdowns last year left passengers stranded around the world.
Also, this month Japan Airlines' maintenance crew noticed white smoke coming from the main battery of a Dreamliner with a battery cell showing signs of melting just two hours before the plane was due to fly.