(Adds Oman, Malaysia, Norway; Boeing shares; public concerns)
* Four more nations suspend Boeing 737 MAX
* Relatives await identification of 157 crash victims
* Ethiopian Airlines Flight 302 black boxes found
* Second disaster with a 737 MAX jet in recent months
ADDIS ABABA/SINGAPORE, March 12 (Reuters) - Singapore, Australia, Malaysia and Oman became the latest nations to suspend Boeing 737 MAX aircraft on Tuesday, while identification of the Ethiopian crash's 157 victims dragged and black boxes were yet to yield the cause.
Sunday's disaster - following another fatal crash of a 737 MAX jet in Indonesia five months ago - has caused alarm in the international aviation industry and wiped billions of dollars off the market value of the world's biggest planemaker.
But experts say it is too early to speculate on the reason for the crash or whether the two are linked. Most crashes are caused by a unique chain of human and technical factors.
Given problems of identification at the charred disaster site, Ethiopia Airlines said it would take at least five days to start handing remains to families.
The victims came from more than 30 different nations, and included nearly two dozen U.N. staff.
"We are Muslim and have to bury our deceased immediately," Noordin Mohamed, a 27-year-old Kenyan businessman whose brother and mother died, told Reuters.
"Losing a brother and mother in the same day and not having their bodies to bury is very painful," he said in the Kenyan capital Nairobi where the plane had been due.
Flight ET 302 came down in a field soon after takeoff from Addis Ababa on Sunday, creating a fireball in a crater. It may take weeks or months to identify all the victims, who include a prize-winning author, a soccer official and a team of humanitarian workers.
The United States has said it remained safe to fly the planes, and Boeing has said there is no need to issue new guidance to operators based on the information it has so far.
Ethiopian Airlines has grounded its four other 737 MAX 8 jets as a precaution and aviation authorities in Singapore, Australia, Malaysia and Oman followed China, Indonesia and others to temporarily suspend Boeing 737 MAX aircraft in and out of their airports.
Anxiety was also evident among some travellers, who rushed to find out from social media whether they were booked to fly on 737 MAX planes - the same model involved in the Lion Air crash off Indonesia that killed 189 people in October.
"Three of my colleagues have had clients asking if their flight was operated by that aircraft," said an agent at the Nairobi office of Carlson Wagonlit Travel.
Black box recorders were found from the Ethiopian crash site on Monday, but it was unclear where they would be looked at.
So long as the recordings are undamaged, the cause of the crash could be identified quickly, although it typically takes a year to fully complete an investigation.
Nearly 40 percent of the in-service fleet of 371 Boeing 737 MAX jets globally is grounded, according to industry publication Flightglobal. That includes 97 jets in biggest market China.
Boeing shares fell 5 percent on Monday, and another 3 percent in pre-market trading on Tuesday.
The U.S. Federal Aviation Administration (FAA) issued a "continued airworthiness notification" for the 737 MAX on Monday to assure operators, and detailed a series of design changes mandated by Boeing after the Indonesia crash.
Boeing said it had been working with the FAA following the Lion Air crash to enhance flight control software that would be deployed across the 737 MAX fleet in the coming weeks.
The MAX 8 has new software that automatically pushes the plane's nose down if a stall is detected. There is no evidence so far whether the system was involved in the Ethiopia crash, though experts said this would be a focus of the investigation.
The new variant of the 737, the world's best-selling modern passenger aircraft, could become the workhorse for airlines around the globe for decades and another 4,661 are on order.
In Latin America, Gol in Brazil temporarily suspended MAX 8 flights, as did Argentina's state airline Aerolineas Argentinas and Mexico's Aeromexico .
In Asia, South Korean budget carrier Eastar Jet said it would temporarily ground its two 737 MAX 8s from Wednesday, while India ordered additional checks on 737 MAX 8 aircraft but said a review found "no significant concern".
Vietnam state media reported the aviation regulator would not issue licences to local airlines to operate the 737 MAX until the cause of the Ethiopian crash was known.
Still, major airlines from North America to the Middle East kept flying the 737 MAX. Southwest Airlines Co, which operates the largest fleet of 737 MAX 8s, said it remained confident in the safety of all its Boeing planes even as it fielded queries from customers.
And in Europe, Norway's Civil Aviation Authority said it was confident of passenger safety on Norwegian Air's fleet of 18 MAX jets, given dialogue to ensure it implemented training and other procedures after the October crash.
Former FAA accident investigator Mike Daniel said the decision by regulators to ground the planes was premature. "To me it's almost surreal how quickly some of the regulators are just grounding the aircraft without any factual information yet as a result of the investigation," he told Reuters.
( Additional reporting by Aradhana Aravindan in Singapore; Katharine Houreld in Nairobi; Eric Johnson in Seattle; James Pearson in Hanoi; Alexander Cornwell in Dubai; Heekyong Yang in Seoul; Tracy Rucinski in Chicago; Tim Hepher in Paris; Writing by Andrew Cawthorne; Editing by Georgina Prodhan and Jon Boyle)