According to official sources, Riyadh will adhere to its long-standing policy aimed at keeping global markets well supplied to stabilise prices, Reuters said on Monday.
"I am sure nothing will change regarding Saudi Arabia's oil policy," one source said.
Top officials from the Organisation of the Petroleum Exporting Countries (Opec) also expressed confidence that the newly appointed King Abdullah would stay the course he charted over the past decade.
"I believe that there is confidence that his (Fahd's) brothers, the leaders of Saudi Arabia, will adopt the same approach and the reaction of the markets to this sad news will calm down," Opec chief and Kuwaiti Oil Minister Sheikh Ahmad al-Sabah said.
"The shock in the market because of the death of King Fahd will be temporary," said Iranian Oil Minister Bijan Zanganeh.
"Because Saudi Arabia's policy was conducted by Crown Prince Abdullah, naturally there should be no change in the country's policy."
Saudi Arabia, Opec's leading producer, would prefer to see US oil prices below $50 a barrel, a level regarded as too high for a healthy world economy.
US crude oil jumped to $61 a barrel after the announcement of the death of Fahd.
To keep world markets sufficiently supplied, Riyadh is pumping about 9.5 million barrels per day (bpd) of crude and has vowed to keep spare production capacity of 1.5 million to two million bpd to meet any supply shortfalls.
Saudi stock market
Meanwhile, the Saudi stock market, the largest in the Arab world, briefly suspended trading and was down almost 2% after reopening.
The stock market bounced back on confirmation of Fahd's death.
The exchange's head of market information, Musaed Al-Nimr, said there would be no further disruption to trading after the king's death.
"Trading will continue as usual today and in the next days," he said.
Saudi Arabia's stock market, the Arab world's most capitalised, has soared this year on the back of the windfall revenues earned by the world's biggest oil producer and exporter.