The review by the FAA will look at the design and manufacture of the planes.
It is not clear whether the planes in the air at the moment will be grounded.
An electrical fire, a brake problem, a fuel spill and cracks in the cockpit’s windshield have affected Dreamliner flights in the past week.
“We are absolutely confident in the reliability and performance of the 787,” Boeing spokesman Marc Birtel said.
“We are working with the FAA and our customers to ensure we thoroughly understand any introductory issues that arise.
“While we take each issue seriously, nothing we’ve seen in service causes us to doubt the capabilities of the airplane.”
The Boeing 787 Dreamliner is one of the most advanced aero planes ever created. Much of it is made from very strong, light carbon-fibre composite material.
However, a spate of technical issues has hurt its image. On Friday, two new problems were found, adding to Boeing’s woes.
Last month, the head of Qatar Airways criticized Boeing over several manufacturing faults that have resulted in the grounding of one of its three 787 Dreamliner aircraft.
Boeing has delivered 50 of the 787s, starting in late 2011, and has orders for nearly 800 more. To get through the backlog, Boeing is increasing production to build 10 of the planes per month by the end of the year.
By comparison, it builds more than one 737, Boeing’s best seller, every day.
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