"There have been a lot of them [attempts]," he said. "Do not come to me. Anyone who does, I will delete your names from the list."
He said it was not fair when people criticised him over his role in appointing the new charter drafters after the previous draft got rejected.
The PM said any comments should be made by members of the new NRC when in session so the drafters can take them into consideration.
"I'd like to say to Abhisit [Vejjajiva]: I don't want to cling on to power. But there's a lot of problems, so you have to help me," he said.
Prayut was speaking at the opening ceremony of a meeting on the 12th National Economic and Social Development Plan, which Abhisit also attended.
Prayut said he would discuss selection of the council's members this week along with the make-up of the new Constitution Drafting Committee. He did not rule out excluding politicians from the council, saying it was up to them if they want to seek a seat on it.
Prayut said the list of the council's 200 members had not yet been finalised, adding that every relevant group - such as politicians, public servants and former NRC members - were being considered and grouped.
Those members would help carry on the work until the next government was elected, he said, adding that the strategic committee would also pass on work to the next government if it were functioning.
In a related development, Deputy Prime Minister Wissanu Krea-ngam said he had no idea about a rumour that 44 NRC members who voted down the draft charter would gain seats on the new council.
He also denied any knowledge about a rumour about a proposal for five officials from each ministry to be on the council.
However, Interior Minister Anupong Paochinda said the ministry was preparing to submit a list of five NRC candidates as requested by Prayut.
Senior political scientist Sukhum Nualsakul, the former rector of Ramkhamhaeng University, said public servants on the NRC would not represent the people's voices and would not respond to the people's demands like elected politicians. However, he said the junta could appoint anyone because it had the power.