Nayef has already run the kingdom on a daily basis for extended periods in recent years, during absences of both King Abdullah and Crown Prince Sultan, who died on Saturday.
Given the king's age and health problems, the new crown prince is likely to assume an even more active role immediately.
An Allegiance Council of the ruling family, set up by the king in 2006, is expected to approve a new crown prince after mourning for Sultan ends on Thursday. It can step in if anything befalls the ruler before an heir is named.
"There is an institutionalised mechanism in place," said Hossein Shobokshi, a Saudi columnist. "The Crown Prince had been deteriorating for some time so they haven't been caught by surprise. It should be extremely orderly.
"We had been waiting for this development and things will be announced from a protocol point of view after the mourning period is over."
At stake is the stability of a security ally of the United States which wields great influence over Sunni Mohammedans through its guardianship of Islam's holiest sites in Mecca and Medina.
The kingdom stood opposed to the Arab Spring uprisings that caused instability in neighbouring Yemen and Bahrain, fearing they might create openings for major regional rival Shia Mohammedan Iran.
Abdullah accepted the condolences of visiting leaders from his seat at Tuesday's funeral, wearing a surgical mask barely a week after a back operation.
Among mourners who greeted him after a prayer recital was Iran's Foreign Minister Ali Akbar Salehi. A US delegation led by Vice President
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is expected in Riyadh on Thursday.
Nayef was later shown on television meeting the king of Jordan and brass hats from the United Arab Emirates.
Nayef, born in 1933, is sometimes described by Saudi liberals as an anti-reform conservative who is likely to take a cautious approach to social and political change, while emphasising national security in foreign policy.
He was quoted soon after the Sept. 11, 2001 attacks on the United States as doubting that any of his compatriots had been involved. It turned out that 15 of the 19 hijackers were Saudis.
Some diplomats and analysts say the man who has served as interior minister since 1975 may show a more pragmatic side as crown prince, and eventually as king.
Some 60 per cent of Saudis are under the age of 30 and, with Internet penetration of 44 per cent according to internetworldstats.com, are increasingly outward looking.
King Abdullah's cautious reforms were opposed by conservative holy mans and have aimed at creating more private sector jobs, reducing the role of religion in education and improving the prospects of Saudi women.