Deputy Agriculture Minister Thammanat Prompao was responding to a report by the Sydney Morning Herald, based on court records and interviews, that he was arrested in 1993 and convicted of conspiracy to import heroin.
Prayuth, questioned by reporters after Tuesday's Cabinet meeting, declined to comment directly on the issue.
Thammanat, a power broker in northern Thailand, is generally credited with having helped Prayuth's ruling Palang Pracharath party perform well in the region in the March general election. But there apparently was hesitation to appoint him to the Cabinet, since it was reported that an offer to name him minister of labor had been withdrawn because of his reputation as an "influential person," a Thai euphemism for shady godfather-type figures.
The Sydney Morning Herald report said Thammanat, then using the name Manat Bophlom, pleaded guilty in 1993 to involvement in trafficking 3.2 kilograms (7 pounds) of heroin into Australia. Three alleged accomplices — two Australians and one Thai — were also charged.
The newspaper said evidence showed Thammanat played a major part in the operation. However, he was given a relatively lenient six-year sentence after cooperating with the police investigation, it said. He was reportedly released after serving four years and then deported.
When asked by reporters Tuesday if he planned to step down from his post, he replied, "Why would I resign?"
He said he had already publicly clarified the case, and that under an agreement made with the Australian police and courts, he could not give further information.
Thammanat said he would focus on who exactly gave information to the Australian reporter, because that person must have intended aim to discredit him politically.
"If they have a problem with me, they should fight me face-to-face," he said. "They do not need to hide like this. I do not mean I intend to actually punch him, but I just want to discuss the real thing, not some mumbling over a story from the past. From now on, I will not respond to those talking about my past, but I will use legal channels."
Thammanat has been linked to several questionable affairs. After he returned from Australia, he was arrested in connection with a killing, and released following an acquittal after spending two years in jail. He was also associated with an army clique that allegedly acted as a sort of mafia in northern Thailand.
Last year, he was connected with a massive bitcoin fraud case, but was not accused of any crime.
When rumors of Thammanat's drug conviction began circulating in July, Deputy Prime Minister Wissanu Krea-ngam said a legal ban on people convicted of narcotics offenses serving in the Cabinet would not apply in cases in which they were convicted by foreign courts.
Thammanat is the most prominent Thai politician to be accused of links to drug trafficking since 1992, when northern politician Narong Wongwan had his nomination to become prime minister scuttled when it was revealed that the United States had refused to give him a visa over suspicions he was involved in the illicit trade. No charges are known to ever have been lodged against Narong.