Police say they will not be taking further action over comments made by Nigel Farage in a speech to supporters.
Gwent Police said they received complaints from the public after a video on social media showed the Brexit Party leader saying “we’ll take the knife” to civil servants.
In a tweet, Alliance Party MEP Naomi Long suggested the address in Newport was a “an incitement to violence”.
Police said the comments did not constitute a criminal offence.
Mr Farage’s address to delegates and party members came during the Brexit Party Conference tour on 21 September.
In a video of the address, the MEP can be heard saying the bosses of the ports of Calais and Dover report they are “100% ready for Brexit in whatever form it comes”.
Mr Farage added: “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.”
The language used by politicians over Brexit has come under the spotlight this week, with a number of MPs during Commons debates on Wednesday and Thursday criticising the prime minister’s choice of words.
Referring to Mr Farage’s speech, Ms Long, one Northern Ireland’s three representatives in the European Parliament, sent a tweet to police on Friday evening.
It asked them to “confirm that you intend to investigate this clear case of incitement to violence against staff in the Civil Service?”
Gwent Police said it was “looking into” the allegations.
Within hours, it issued a statement saying: “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.”
The Brexit Party has not yet responded.
In a tweet, Mr Farage posted a link to a Sky News report about the police inquiry, writing: “I should have said ‘take the axe’, which is a more traditional term for cuts.”