King Bhumibol Adulyadej died on Thursday and the crown prince wants more time to mourn his father.
Former Prime Minister Prem Tinsulanonda is standing in as regent.
Current Prime Minister Prayuth Chan-ocha sought to reassure Thais about the succession in a TV address on Saturday, saying they should not worry.
This issue was discussed when Crown Prince Vajiralongkorn summoned the regent and Gen Prayuth for an audience, according to Gen Prayuth.
The 64-year-old crown prince “asked the people not to be confused or worry about the country’s administration or even about the succession”, Gen Prayuth said in his TV statement.
“He said at this time everyone is sad, he is still sad, so every side should wait until we pass this sad time.”
Questions about the crown prince’s capabilities have been raised in the past, although the strict lese-majeste laws prevent any open discussion of these.
Gen Prayuth took power in a military coup in 2014 which overthrew the civilian government. He has promised elections next year.
The monarchy is seen as a unifying force in Thailand at times of political upheaval and King Bhumibol, who died aged 88, was a figure revered by many Thais.
The military government has made clear that Crown Prince Vajiralongkorn will be the new king, reports the BBC’s Jonathan Head in Bangkok, but it just isn’t clear when this will happen.
The military has traditionally been intensely loyal to the monarchy.