The tweet, which has since been deleted, drew a swift rebuke from his employer, United Airlines.
"We are appalled by comments advocating harm to any person," said airline spokesperson Mary Clark. "They do not represent United Airlines and we are looking into the matter further."
United subsequently suspended Folk, pending the results of its investigation.
The tweet also sparked a backlash on social media.
But Folk later said the tweet wasn't meant to be taken literally and was merely "hyperbole."
Folk said in a telephone interview with The Associated Press he still wants Clinton to go on trial, but he doesn't want her executed.
"It could have been said a little bit better," Folk said. "I regret the tone, and the second part of that tweet.
"The biggest misconception is that for some reason, everybody thinks I made a death threat, which I did not. Clearly it was not that."
The Justice Department announced earlier this month Clinton would not be prosecuted over her handling of classified information.
Folk said he sent the tweet after watching a video of testimony before a U.S. House committee over the Clinton emails.
"I watch something like that that gets me riled up, I usually just sleep on it and maybe do something the next day," he said. "I should have done that."
The state Democratic Party has called for his resignation. Folk said he won't resign.
Folk also said he hasn't directly talked with the state GOP about it.
Folk, who said he's received death threats over the comments, is seeking a third term. The Martinsburg resident ran unopposed in the May Repupblican primary and will face Democrat and Berkeley County Sheriff Kenny Lemaster in November.