The precautionary move in Japan came after an All Nippon Airways Dreamliner on a domestic flight made an emergency landing due to a faulty battery and smoke, the latest in a string of safety scares for the next-generation 787.
Aviation regulators in the United States, Japan and India have launched probes but Boeing insists the plane is safe. And airlines that have bet big on the plane quickly expressed confidence the firm would resolve any issues.
British Airways, which has 24 Dreamliners on order, reaffirmed a statement from last week that it was "committed to taking delivery of the aircraft".
Scoot, a budget long-haul unit of Singapore Airlines, said there was no change to its order for 20 of the high-tech aircraft.
"Boeing has kept us fully informed about the performance of the 787 since we committed to acquire the aircraft," the company said in a statement.
"We are confident that Boeing's ongoing performance monitoring and external review process will identify and resolve any issues, and look forward to taking delivery of our first 787 on schedule in late 2014."
Australia's Qantas said it was confident that any problems would be resolved before it took delivery of 15 Dreamliner jets destined for its low-cost offshoot Jetstar in the second half of this year.
Korean Air, which has 10 B787-9 planes on order, said it carried out stringent tests before putting any new aircraft into service and it still intended to operate the Dreamliner from late 2016.
"Problems are bound to occur when new aircraft are being developed and put into operation. Recent problems involving the B787 are no different," a Korean Air spokesman said.
"The B787-9 model we are about to put into service beginning late 2016... is better than any other aircraft in terms of efficiency and safety and will have no problems operating."
Ethiopian Airlines, which is the first African airline to operate the aircraft, said it was "pleased with the performance of our Dreamliners".
"Like any new technology aircraft entering into service, it is normal to encounter some minor bugs here and there," said the CEO of the airline, which has ordered 10 of the planes and already has four in regular operation.
A spokesman for LOT Polish Airlines, which has two Dreamliners and "nothing has changed" with its plans for more, even if LOT has also had "minor problems" with the aircraft.
A LOT official added that Japan's Dreamliners were produced well before the planes it operates.
"They're experiencing battery issues that have since been eliminated by Boeing," he said.
Wednesday's incident followed a fire on a Japan Airlines (JAL) aircraft last week after it landed in Boston, two fuel leaks on another JAL Dreamliner and a cracked cockpit window that forced the cancellation of a Dreamliner flight in Japan.
Both ANA and JAL said they would ground their entire 787 fleets for safety checks through Thursday at least.
But ANA - the Dreamliner's launch customer in 2011 - said it was sticking to its plan to roll out the plane across its fleet. It has ordered 66 so far.
The fuel-efficient Dreamliner has been coveted in Asia to combat soaring energy costs. JAL has another 38 of the planes on order.
Air China has ordered 15 of the planes, while China Southern and Hainan Airlines await deliveries of 10 each.
There was no comment immediately available from the trio, but a smaller Chinese carrier - Xiamen Airlines - said it still wanted the six Dreamliners it has ordered from Boeing.
Air India has taken delivery of five already, but said it would keep flying them as India's aviation regulator investigates the safety issues that have arisen in Japan.
Among other Asia-Pacific customers for the Boeing 787, Indonesia's Lion Air, Air New Zealand and Vietnam Airlines all declined comment.