The US aviation regulator said it would not ground the planes and that a review "shows no systemic performance issues and provides no basis to order grounding the aircraft", but will "take immediate and appropriate action" if issues are identified.
Here is what airlines and regulators worldwide have said:
The Mexican airline said it suspended the operation of its six MAX 8 planes and those flights would be covered by the rest of its fleet.
The company said it remained fully confident in the aircraft. Mechanics' union TWU has urged the company's chief executive to ground MAX 8s.
Australia's Civil Aviation Safety Authority
The regulator said it had suspended the operation of Boeing 737 MAX aircraft to or from the country.
Bermuda Civil Aviation Authority
The British overseas territory's aviation authority said it prohibited MAX 8 and MAX 9 aircraft from its airspace.
Brazil's Air Travel Regulator, Gol Linhas Aereas Inteligentes SA
The Brazilian regulator said it was not grounding the aircraft. Gol, which operates seven MAX 8s, said it was suspending use of the aircraft.
Canada's Transport Ministry, Air Canada, Westjet
Canada has no plans to ground the MAX 8 aircraft but is ready to "act immediately" to suspend flights if new information emerges indicating there is a problem, Transport Minister Marc Garneau said.
Air Canada, which has 24 MAX 8s in its fleet, said it cancelled four flights this week due to the UK Civil Aviation Authority ban on MAX jets. WestJet, which operates 13, is monitoring the situation.
The airline said it had grounded both its MAX 8 jets.
China's Aviation Regulator
The regulator grounded 96 MAX 8s including those operated by Air China, China Eastern Airlines, China Southern Airlines and Hainan Airlines.
The South African airline said it would remove 737 MAX 8 jets from its schedule. It has ordered eight aircraft of this type but has only received one.
European Aviation Safety Agency
The European Union's aviation safety agency has suspended all flights in the bloc by 737-8 and 737-9 airplanes.
The airline whose plane crashed on Sunday, killing all 157 on board, grounded the remaining four of its 737 MAX 8 fleet on Monday.
The company's chief executive officer said Boeing should ground all of its 737 MAX 8 jets until it is established that they are safe to fly.
Civil Aviation Authority of Fiji, Fiji Airways
The airline and the authority temporarily grounded the carrier's two 737 MAX planes, saying they had confidence in the model's airworthiness but would suspend flights out of deference to public concern and regulatory action around the world.
Hong Kong's Civil Aviation Department
The agency said operation of all 737 max aircraft into, out of and over Hong Kong will be temporarily prohibited.
Indian Ministry of Civil Aviation, Spicejet, Jet Airways
India says it will not allow 737 MAX aircraft to enter or transit its airspace. SpiceJet, which has 12 MAX 8s and another 155 MAX planes on order, said it expects to complete the grounding of those planes on Wednesday. Jet Airways said it is not flying the aircraft.
Kazakhstan's Civil Aviation Committee
Kazakhstan suspended 737 Max flights. Only one aircraft of that make is registered in the Central Asian nation, belonging to a privately-owned Scat airline.
Kuwait Civil Aviation
The aviation authority banned MAX 8 aircraft from its airspace, state news agency KUNA said.
Macau's Civil Aviation Authority
The regulator says it is suspending approvals of requests by airlines to use the 737 MAX. There are no such aircraft currently registered in Macau.
Miat Mongolian Airlines
The state airline, which rented one 737 MAX from Feb. 1, grounded the aircraft. It had signed a contract to rent three Boeing 737 MAX 8 aircraft and was planning to rent the other two later this year.
The company will temporarily ground its MAX 8 passenger jets at the advice of European regulators. It operates 18 MAX jets.
Norwegian also said it will seek compensation from Boeing for costs and lost revenue.
New Zealand's Civil Aviation Authority
The regulator suspended MAX aircraft from flying to or from the country, saying Fiji Airways would be the only airline affected.
Russian S7 Airlines said it would ground its two MAX 8 planes starting Wednesday and that the decision would not affect its flight schedules.
Singapore Civil Aviation Authority, Singapore Airlines
Singapore's Civil Aviation Authority suspended operations of all Boeing 737 MAX aircraft in and out of the country. Singapore Airlines said its unit Silk Air, which operates 6 MAX 8 planes, has temporarily withdrawn them from service.
South Korea Transport Ministry, Eastar Jet
South Korea said it is conducting an emergency inspection on Eastar Jet's two MAX 8 jets. Budget carrier Eastar Jet said it would temporarily ground its two 737 MAX 8s from Wednesday.
The US airline said it remained fully confident in the aircraft and was closely monitoring the investigation.
Swiss Federal Office of Civil Aviation
The EU's suspensions of all flights by Boeing 737 MAX 8 is also valid for Switzerland, the Swiss federal office of civil aviation said.
Civil Aviation Authority of Thailand
The regulator said it is suspending the use of the Thai Lion Air's Boeing 737 MAX 9 for seven days due to safety concerns.
Germany's TUI Group, the largest leisure, travel and tourism company in the world, said it was discontinuing all Boeing 737 MAX 8 flights.
Turkey Transport Ministry, Turkish Airlines
The ministry has suspended all flights by the 737 MAX 8 and MAX 9 models, Anadolu news agency said. The announcement came after Turkish Airlines said it had suspended its 12 Boeing 737 MAX aircraft.
UAE General Civil Aviation Authority, flydubai
The civil aviation regulator banned the operation of all MAX models in UAE airspace, Emirates News Agency (WAM) said. Flydubai, which has 11 MAX 8 aircraft in its fleet, according to Flightradar24, is the only UAE airline operating the MAX 8 and MAX 9 aircraft.
UK Civil Aviation Authority
Britain suspended flights of the 737 MAX aircraft over its territory.
Uzbekistan's Civil Aviation Agency
Uzbekistan's civil aviation agency on Wednesday barred 737 Max jets from taking off or landing at local airports for one month.
Vietnam's Civil Aviation Authority
The agency said it banned 737 MAX aircraft from Vietnamese airspace.
The Australian airline said it would continue to work with Boeing; the airline, which does not have any 737 MAX 8 aircraft, said its first delivery was not due until November.
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