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.
We have received a number of comments and concerns from members of the public regarding a video that is circulating on social media. We can confirm this video relates to a visit by Nigel Farage to The Neon in Newport as part of a Brexit Party rally on the evening of 21st September. We are aware of the heightened tensions that exist regarding use of language, and take all allegations and concerns from members of the public very seriously. However, following a thorough assessment, it is our view that the comments in the video, do not constitute a criminal offence. As such, Gwent Police will not be taking any further action.
Brexit Party leader made these comments at a rally last Saturday:
When the president of the port of Calais and the boss of the port of Dover tell you they're 100% ready for Brexit in whatever form it comes I suggest we listen to them and not the overpaid pen pushers in Whitehall who are not doing a neutral job and once Brexit's done we'll take the knife to them. I've had enough of all of it.
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.