The incident prompted regulators around the world to halt flights of the 50 Dreamliners already in service, including two in the European Union that are operated by LOT Polish Airlines.
Battery-related problems are being investigated after warning lights indicated a battery fault on the ANA flight on Wednesday.
European Aviation Safety Agency officials said on Wednesday they were monitoring international investigations of the Dreamliner after ANA and Japan Airlines (JAL) grounded their fleets following several scares.
EU safety body orders Dreamliners grounding
The EU safety body on Thursday followed the US decision to suspend flights of the aircraft pending a safety review.
The only EU airline to so far use 787s on regular flights is LOT Polish Airlines. One of its two Dreamliners was grounded in Chicago after its first overseas flight on Wednesday (16 January).
A LOT spokesman told EurActiv just hours before departure that the company “conducted, preventively, a series of reviews of all systems in both Boeing 787s we have in our fleet. All the tests were completed positively – the systems are efficient and work well.”
The five representatives from the US National Transportation Safety Board, Federal Aviation Administration and Boeing are helping Japanese authorities in the investigation of the aircraft, which remains parked at the side of Takamatsu airport in western Japan.
The Japan Transport Safety Board aims to end its initial checks this weekend, a person familiar with the matter told Reuters.
"The Boeing 787 is an absolutely wonderful aircraft and we will spare no effort to help it get back in the air safely as soon as possible," said ANA spokesman Hideya Oishi.
GS Yuasa Corp, the Japanese company that makes batteries for the Dreamliner, said it also sent three engineers to Takamatsu to help the investigation.
Battery fire in Boston
Troubles began on 7 January when a battery caught fire in the auxiliary power unit (APU) of a JAL 787 parked at Boston Logan International Airport.
The US investigation into that incident is focused for now on the Japanese-made batteries, with no indication the APU - built by United Technologies Corp's Pratt & Whitney - was involved, said a person familiar with the government probe, who was not authorised to speak publicly.
Laura Brown, a spokeswoman for the FAA in Washington, said she could not comment as the issue was part of the investigation.
Regulators in Japan said it was unclear when the Dreamliner could be back in the air. Japan is the biggest market so far for the 787, with ANA and JAL operating 24 of the 290-seat wide-bodied planes, which have a list price of $207 million.