King Salman bin Abdul-Aziz Al Saud's comments come as the oil-rich Sunni kingdom began mourning King Abdullah, who died early today after nearly two decades in power.
"We will continue adhering to the correct policies which Saudi Arabia has followed since its establishment," Salman said in the speech aired on the state-run Saudi 2 television station.
Salman also made an oblique reference to the chaos gripping the greater Middle East as the extremist Islamic State group now holds a third of both Iraq and Syria.
Salman, 79, had increasingly taken on the duties of the king over the past year as his ailing predecessor and half brother, Abdullah, became more incapacitated.
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Salman had served as defence minister since 2011. That made him the head of the military as Saudi Arabia joined the US and other Arab nations in carrying out airstrikes in Syria in 2014 against the Islamic State group, the Sunni militant group that the kingdom began to see as a threat to its own stability.
He takes the helm at a time when the ultraconservative Muslim kingdom and oil powerhouse is trying to navigate social pressures from a burgeoning youth population -- over half the population of 20 million is under 25 -- seeking jobs and increasingly testing boundaries of speech on the Internet, where criticism of the royal family is rife.