King Bhumibol Adulyadej died on Thursday after seven decades on the throne. He was 88.
The prospect of complications in the succession in the politically divided country could alarm financial markets and the military government has been quick to quash any such speculation.
The head of the royal advisory council, a 96-year-old former army chief and prime minister, Prem Tinsulanonda, is standing in as regent while the prince and the country grieve.
Prince Vajiralongkorn held an audience with Prem and Prime Minister Prayuth Chan-ocha on Saturday evening and asked them to pass on his reassurance to the people, Prayuth said.
‘He asked the people not to be confused or worry about the country's administration or even about the succession,’ Prayuth said in a televised address.
‘He said at this time everyone is sad, he is still sad, so every side should wait until we pass this sad time ... When the religious ceremony and funeral have passed for a while, then it will be an appropriate time to proceed,’ Prayuth said.
Mourners dressed in black from across Thailand have flocked to Bangkok's gilded Grand Palace to pay homage to the only king most of them have ever known.
Buddhist monks have been chanting prayers beside his coffin in an imposing throne hall. Monks will chant for 100 days as part of the funeral rites.
The government has not set a date for the funeral but in the past, royal cremations have taken months to prepare.
The government has declared a year of mourning and asked everyone to wear black or white, and to cancel outdoor festivities, for the first 30 days.
Though almost everyone has donned black and the mood is sombre, shopping malls, markets, cinemas and even some bars have been open.
The king, who was the world's longest reigning monarch, has long been revered as a father figure and symbol of unity in a country riven by political crises over the years, most recently by a power struggle between the military-led establishment and populist political forces.
Many Thais worry about a future without him.
Prince Vajiralongkorn does not enjoy the same adoration his father earned over a lifetime on the throne. He has married and divorced three times, and has spent much of his life outside Thailand, often in Germany.
Though the king designated his only son crown prince in 1972, he also raised the possibility of the eligibility of a princess. Thailand's strict lese-majeste laws have left little room for public discussion of the succession.
Prayuth, a former army chief who overthrew a populist government in 2014, has promised an election next year. The government has not said if it might postpone the vote because of the year of mourning.
The military has for decades invoked its duty to defend the monarchy to justify its intervention in politics and it recently oversaw the drafting of a new constitution that grants it oversight of civilian governments.
King Bhumibol's promotion and funding of charitable work throughout rural Thailand endeared him to the population.
‘Everyone should take this time to keep the memories of the past 70 years,’ Prayuth said.