Prayuth heads the ruling junta, or National Council for Peace and Order, that took power after a bloodless coup toppled Prime Minister Yingluck Shinawatra's elected government in May 2014 coup.
Speedboat crash kills three tourists in Thailand
The military had justified the coup, saying it had acted to restore stability after months of street demonstrations in Bangkok had paralyzed Yingluck's government.
"I won't resign. I am the one who lays out the rules for this country," Prayuth told reporters at Bangkok's Government House, insisting Thais should not compare him to British Prime Minister David Cameron who announced his resignation last week after Britain voted in a referendum to quit the European Union.
Ailing Thai king undergoes heart operation
The junta has said it would carry out political and economic reforms before a general election in 2017 that will start a transition back to democracy.
The August 7 referendum will be the first national vote in Thailand since the coup and should provide a test of the junta's popularity, experts said.
Ailing Thai king treated for excess fluid in spine and brain
Groups of all political stripes have denounced the draft constitution as undemocratic, with one major political party urging supporters to vote "no".
The junta has banned criticism of the charter in the run-up to the vote and in May the Election Commission issued rules barring anyone from campaigning for either side ahead of the referendum.
In the latest crackdown on dissidents, a Thai court jailed seven activists on Friday for campaigning against the draft charter, which critics say will enshrine military power and emasculate civilian politics.
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