The former army chief led a coup in 2014 and kept the kingdom under military rule for five years.
Under the junta, a new constitution was drafted before elections were held last year.
Prayut was voted in to lead a civilian government — a win analysts say was tilted by the new charter's provisions.
Thai anti-government protesters say the whole process was a stitch-up and are calling for parliament to be dissolved, the constitution rewritten and an end to the harassment they are facing.
They also have a list of 10 demands for the monarchy, including throwing out a defamation law that shields the powerful royal family from criticism.
The law is one of the harshest of its kind in the world, carrying a jail sentence of up to 15 years per charge.
Discontent has been simmering since February when the leaders of an opposition party, popular among young people, were banned from politics.
Many protesters say the move against the Future Forward Party was politically motivated.