Saudi Crown Prince Nayef bin Abdul Aziz, a half brother of King Abdullah, died on Saturday, the royal court said, leaving the oil powerhouse with no apparent successor to the throne.
Prince Nayef, a long-serving interior minister, "died outside" Saudi Arabia having recently left the Gulf state for medical treatment, said a statement carried by state media, including Al-Ekhbariyah Television and SPA news agency.
His funeral would be held on Sunday after sunset prayers in the Muslim holy city of Mecca in western Saudi Arabia, after his body is repatriated, it added.
The 79-year-old prince died of "cardiac problems" while he was in Switzerland, at his brother's residence in Geneva, according to a medical source in the city who requested not to be identified.
US President Barack Obama offered King Abdullah, the royal family and the Saudi people his "deepest condolences".
"Under his leadership, the United States and Saudi Arabia developed a strong and effective partnership in the fight against terrorism, one that has saved countless American and Saudi lives," Obama said in a statement issued by the White House.
French President Francois Hollande said his country lost a "friend" who "contributed in a decisive way to Franco-Saudi relations," according to a statement from his office.
Nayef's death, just eight months after he replaced his late brother crown prince Sultan, raises the issue of succession because of the advanced age of the first line of apparent heirs, at a time of turmoil rocking the Arab world.
King Abdullah himself is 88 and ailing, and nobody is officially in line to replace Nayef.
However, his brother Prince Salman, 76, who took over the portfolio of defence minister after Sultan's death, appears to be a strong candidate.
The monarch established in 2006 the allegiance council, a body of around 35 senior princes, as a new succession mechanism aimed in the long term to choose the crown prince.
"No doubt, the new crown prince will be appointed by the allegiance council," said Anwar Eshqi, head of the Jeddah-based Middle East Centre for Strategic Studies.
"All expectations point to Prince Salman to succeed Prince Nayef for his experience in administration, security and politics," he said.
But the new commission had not been activated when Nayef was chosen as crown prince, according to political scientist Khaled al-Dakheel, who argued that naming his successor is a chance to put the new body to use.
"Prince Nayef was named under the old system, without activating the allegiance council system," he said, pointing to the royal decree that established the council and postponed its use until after Abdullah's death.
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"This is a chance to activate the allegiance council system... which provides a legal foundation for a peaceful power transfer within the family and leaves no room for surprises. This is important for state stability," Dakheel said.
Nayef, who spearheaded Saudi Arabia's clampdown on Al-Qaeda following a wave of attacks in the conservative kingdom between 2003 and 2006, became heir to the throne in October last year.
He was the middle prince of the Sudairi Seven, the formidable bloc of sons of King Abdul Aziz by a favourite wife, Princess Hassa al-Sudairi.
Prince Nayef travelled abroad several times this year for medical reasons, including to Algeria, the United States and Switzerland, where he was shown on television in Geneva three days ago greeting supporters.
The nature of his illness has not been made public.
Less than two weeks ago, his brother Prince Ahmed bin Abdul Aziz was quoted as saying in a Saudi daily that the crown prince was in "good health" and would "soon" return to the kingdom.
On May 26, SPA reported that Prince Nayef had left the country for medical tests abroad for the second time in less than three months, without naming his destination.
In March, the royal palace said he was in Algeria on holiday after the results of medical tests carried out in the US city of Cleveland were reported as "reassuring."
He returned to Saudi Arabia from Algeria on April 10.
Seen as more conservative than King Abdullah, Prince Nayef was a staunch defender of the Saudi dynasty who resisted any form of opposition.
He ordered and oversaw a fierce crackdown on Al-Qaeda, forcing the jihadist group's leaders and militants to flee to Yemen, from where they continue to threaten Saudi interests.
As interior minister, Prince Nayef also dismantled charitable organisations that collected donations for the terror network.
He was known to be close to the religious establishment, and has opposed introducing elections to vote in members of the all-appointed consultative council, as well as being against allowing women to vote in municipal elections.
During his 37 years as interior minister, Nayef also made sure that women were not allowed to drive, decreeing in 1990, following a daring demonstration in cars by 47 Saudi women, that women were banned from getting behind the wheel.
Jordan, meanwhile, declared a day of national mourning on Sunday while Iraqi President Jalal Talabani said Nayef "worked to strengthen ties between all Arab and Islamic countries."