Police said they have been "looking into" comments made by Nigel Farage at a Brexit Party rally in Newport last week.
The Brexit Party leader said "we'll take the knife" to "the overpaid pen pushers in Whitehall".
Gwent Police said "following a thorough assessment" the comments do not constitute a criminal offence.
Brexit Party leader made these comments at a rally last Saturday:
Nigel Farage's speech from the Newport conference can be seen here:
Referring to the comments, Nigel Farage tweeted just after 2pm today: "I should have said ‘take the axe’, which is a more traditional term for cuts."
The Brexit Party has been approached for comment.