The authorities announced on Sunday that the identities of 56 of the 69 fatalities had been conclusively established.
Fifty-four were Spanish citizens, one was from France and another from Portugal.
"It is expected that the remaining victims will also be identified within the coming hours. These are likely to be exclusively people from abroad," the authorities said in a statement, citing missing persons reports that are still pending.
They are believed to be four nationals from the United States, two each from Japan and Australia and one each from Canada, Mexico, Argentina, the Czech Republic and Tunisia.
The identities of 51 of the 56 identified victims have been communicated to their relatives.
Those victims included 33 men and 18 women.
Forty injured passengers are still receiving hospital treatment, 17 of them in intensive care.
The accident occurred when a high-speed train collided with a stationary train near the municipality of Urda in the province of Toledo about 130km south of Madrid.
The railway line between Madrid and Andalusia remains closed in both directions.
The Iberia airline is providing additional flights at capped prices.
