Gen Prayuth said this after receiving a royal command appointing him the country's 29th prime minister in a ceremony held at army headquarters on Monday morning.
He initially said the cabinet list would be completed in October but then corrected himself, saying he actually intended to say the list would be finished and forwarded to His Majesty the King for royal appointment in September.
The prime minister said in handling the country's administration, the government and the National Council for Peace and Order (NCPO), of which he is also chairman, would be in close consultation.
The government and the NCPO would not infringe on each other's responsibilies. but would act as check-and-balance to ensure transparency, he said.
He pledged to strengthen every system to effectively counter corruption, saying that the people should not attach too much importance to individuals.
The people would have to play the most important role in pushing for the administration to effectively solve the country's problems in areas such as security, the economy and social, cultural, legal and judicial affairs - where problems had long been accumulating and left unsolved - in order to be fully prepared for entry into the Asean Economic Community at the end of 2015, Gen Prayuth said.
"The government, NCPO and the people must join hands to quickly solve these problems without obstructing or getting rid of one another.
"We want the National Reform Council (NRC) to comprise a variety of people to push for reforms in 11 areas. We don't want our move toward democracy to derail.
"We must together build the country's future, without causing any more problems," said the prime minister.
Gen Prayuth pledged to perform the duties of prime minister honestly and sincerely by adhering mainly to the interests of the country and the people.