It is understood that all eight airlines that have received the Dreamliner have taken the aircraft out of service while Boeing joins the US and Japanese authorities in trying to identify and solve a battery problem.
Analysts said Boeing could end up paying compensation of up to $125m to airlines should the grounding of the Dreamliner last months rather than weeks.
All Nippon Airways and Japan Airlines both took the decision to ground planes after reporting incidents on the new -aircraft, and others followed suit after the US Federal Aviation Administration said last night that it was instructing American carriers not to fly the aircraft. United Airlines is currently the only US airline operating the 787, with six planes in service.
The statement from the FAA suggested that it expected aviation authorities worldwide to take similar action. The other airlines that have received Dreamliners are Air India, Ethiopian Airlines, Chile's LAN Airlines, LOT Polish Airlines and Qatar Airways.
Qantas Airways cancelled one of the 15 Dreamliners it had ordered, according to reports yesterday (Thursday), in what would be the first cancellation since the safety crisis emerged.
Jim McNerney, Boeing's chairman, president and chief executive, said the company "deeply regrets the impact that recent events have had on the operating schedules of our customers and the inconvenience to them and their passengers".
He added: "The safety of passengers and crew members who fly aboard Boeing aeroplanes is our highest priority.
"Boeing is committed to supporting the FAA and finding answers as quickly as possible. The company is working around the clock with its customers and the various regulatory and investigative authorities. We will make available the entire resources of The Boeing Company to assist.
"We are confident the 787 is safe and we stand behind its overall integrity."
An ANA pilot reported that the controls warned of an error with a lithium ion battery, and smoke was detected in the cockpit.
Airlines around the world have ordered a total of 848 Dreamliners, which first entered service in late 2011 - three years later than planned.
Wall Street's reaction to the 787's travails was relatively muted. Boeing's shares were little changed at $74.21 in New York in early afternoon trading. Given that the introduction of the Airbus A380 was also dogged by problems, investors are giving the US company the benefit of the doubt.
There was better news for Boeing after it regained the top spot from Airbus as the world's biggest aircraft maker.
However Airbus secured 833 orders last year, far exceeding a sales target of 650. It compared with sales of 1,203 at Boeing.
Airbus has a target of 700 orders this year, excluding any cancellations, and expects to deliver more than 600 aircraft.