World leaders are gathering in Saudi Arabia to pay their respects after the death on Friday of King Abdullah.
British Prime Minister David Cameron has joined French President Francois Hollande in Riyadh. A US delegation, led by Vice-President Joe Biden, is due to arrive.
King Abdullah died aged 90. He was buried in an unmarked grave in Riyadh after Friday prayers.
King Salman, 79, pledged continuity after his accession to the throne.
He also moved swiftly to appoint heirs and ministers, including one prince from the ruling dynasty’s third generation.
The visitors from around the world will all be looking to take the measure of the character, mood and intentions of the new monarch, BBC Arab Affairs editor Alan Johnston says.
King Abdullah died on Friday, weeks after being admitted to hospital with a lung infection.
Gulf leaders, Turkey’s President Recep Tayyip Erdogan and Pakistan’s Prime Minister Nawaz Sharif attended the funeral.
Why Saudi matters
US President Barack Obama paid tribute to Abdullah as a leader who “was always candid and had the courage of his convictions”.
Mr Obama is shortening his three-day trip to India - dropping a visit to the Taj Mahal - and will now fly to Saudi Arabia on Tuesday to meet the new king.
UN Secretary-General Ban Ki-moon praised Abdullah’s work “to promote dialogue among the world’s faiths”.
However, human rights groups said Saudi Arabia’s human rights record had been dismal under Abdullah and urged Salman to do more to protect freedom of speech and women’s rights.
Amnesty International spokesman Neil Durkin described Abdullah’s human rights legacy as “disastrous”, saying that “endemic torture in police cells and in prisons” remained.
New appointments
Within hours of acceding to the throne, King Salman - a half-brother of the late king - vowed to maintain the same policies as his predecessors.
“We will continue adhering to the correct policies which Saudi Arabia has followed since its establishment,” he said.
He named another of King Abdullah’s half-brothers, Muqrin, as the new crown prince.