The Dreamliner's reliability rate is now around 98 percent, meaning that two out of every 100 flights is delayed, which is above the 97 percent reported in October but still short of the firm's target, Fleming told a news conference in Oslo where Norwegian Air Shuttle ASA, one of his most troubled customers, is based.
"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," Fleming said.
"The 777 today flies at 99.4 percent ... and that's the benchmark that the 787 needs to attain.
"We introduced the 777 in 1995 and it was in the 1999 timeframe that we saw sustained performance over 99 percent in that fleet ... to get the fleet above 99 percent you have to keep working every day, so my guess is that it will be similar to what we had with the 777," he added.
Norwegian Air Shuttle, the only European budget carrier to fly long haul, has been plagued by problems with its first three Dreamliners with a series of breakdowns last year leaving passengers stranded.
The Dreamliner was supposed to be a game-changer for the aviation industry as its lighter body and sophisticated engines cut fuel consumption by 20 percent.
But it has been beset by problems including a battery fire that grounded all 787s in service for three months last year and forced Boeing to re-design the innovative lithium-ion battery and enclose it in a stainless steel containment box capable of withstanding an explosion. It also equipped the battery with a metal exhaust tube to vent fumes and gases outside the jet if the battery were to overheat.
Although the batteries have worked reliably since then, this month Japan Airlines' maintenance crew noticed white smoke coming from the main battery of a Dreamliner, with a cell found to be showing signs of melting just two hours before the plane was due to fly.
"We recently had a single-cell failure in a battery on another customer's airplane and we didn't get propagation of that to other cells, other cells continued to function," Fleming said. "The containment box worked as supposed to and the vapour vented overboard as supposed to."
But Fleming said the battery has not suffered an in-flight failure since the redesign and Boeing could still change the battery's design based on the conclusions of the investigation into the latest incident.
"We didn't assume we would never have another cell failure. We always assume we're going to have a failure and we design the airplane with a redundancy," Fleming said.
Other issues on the Dreamliner still facing Boeing include the reliability of flight controls, particularly for the wing spoilers, brakes and electrical power components.
Fleming said any compensation issue with Norwegian Air would be discussed privately but the plane maker takes responsibility for the technical faults.
"When our airplane breaks and our service doesn't deliver on what it's supposed to, we take responsibility," he said.
(Balazs Koranyi and Joachim Dagenborg -Reuters)