Spain's Prime Minister Mariano Rajoy offered his condolences to the families of the all-Spanish crew and said the crash was a blow to an industry that was important to Spain — and to Europe.
"I hope there will be maximum transparency when explanations are made as to what happened here. That's what I'm going to ask of Airbus," Rajoy said.
Seville is the final assembly point for the A400M — a 20-billion-euro program that saw its first deliveries in 2013. Some 194 aircraft have been ordered by eight countries — including Spain — to replace their aging Hercules fleets.
Airbus said the plane that crashed was scheduled to be delivered to Turkey in June as the country's third such aircraft.
Last month Airbus dismissed the head of its military program after governments including Germany, France and Turkey complained about delays in the A400M.
Britain's Ministry of Defense said Saturday it was suspending the use of the Airbus A400M after the crash.
The ministry said use of Britain's two A400M's had been "temporarily paused" as a precaution.
James Darcy, a spokesman for Airbus in the U.S., said the crash was the first for the aircraft since it entered service with the French Air Force in 2013.
He said Airbus Defense and Space has been ramping up production of the plane "as part of the normal planned growth for the program." The target for this year is 14 aircraft, up from eight last year, he said.
The origins of the plane date back to the 1980s, when NATO countries anticipated a need for larger and longer-ranged aircraft, said Richard Aboulafia, an aviation analyst at aerospace consultancy Teal Group.
"The main difference is it's bigger and longer-range and it's new, as opposed to the very old aircraft they had been flying," he said.
A spokeswoman for Spain's Interior Ministry at the scene of the crash told The Associated Press that the two crew members who had been rescued alive had been taken to a hospital in Seville — one suffering from a head injury but still conscious and the other with serious burns. She spoke on condition of anonymity because her name is not allowed to be cited in the press.
Spain's airport authority AENA said that Seville airport was closed for just over 1 1/2 hours as its fire crews went to attend the plane crash outside its perimeter fence. Three incoming flights to Seville were diverted to Malaga and Jerez airports, AENA said.
The crash also knocked out power at an industrial estate in the suburb of Carmona, AENA said.
According to the Aviation Safety Network, the mishap is the first ever crash involving an A400M.
--CNBC contrbuted to this story.