Mr Virues is understood to have died last week, while Mr Martinez - who was still alive on Sunday when he was found - died later from injuries.
"We want them home as soon as possible," Mr Virues-Ortega said.
The family were told last night an autopsy had been completed on one of the two men in Marrakech.
"We are worried that this process may delay them more. The families are going through great suffering."
At the beginning of this week, Spanish media accusations from the Spelunkers Federation of Andalusia in southern Spain that Morocco had delayed accepting help from experts to recover the hikers, possibly costing the life of one of the climbers.
Spanish Prime Minister Mariano Rajoy, however, declined to comment on those reports and said authorities were in contact with their Moroccan counterparts from the beginning and had immediately offered a team of police experts to rescue the three.
"(Moroccan authorities) understood" and there's no reason to believe any differently "that they could do it with their own means. It wasn't easy because these kind of things are never easy," Mr Rajoy told Spanish National Radio on Monday.
Morocco's government spokesman could not be reached for comment.
Mr Virues-Ortega had 25 years experience in mountaineering, caving, canyoning and climbing, Mr Virues said.
"He's been the leader of many expeditions in South America, North America - he's been to the Alps, Andes, Iceland, Morocco and many other places over the years. This was a tragic loss."
Mr Virues said his youngest brother and a cousin, who were both part of the larger expedition group, remained in Morocco as the investigation into the climbing deaths continued.
- additional reporting AP