The incident happened onboard a train from Erith to London Bridge at around 3pm on September 23.
British Transport Police have since been investigating a man in possession of an offensive weapon and a serious public order offence.
Officers believe the man in the images may have information which could help with their investigation.
Anyone who recognises him is asked to contact BTP by texting 61016 or by calling 0800 40 50 40, quoting reference 2400123973.
Alternatively, you can contact Crimestoppers anonymously on 0800 555 111.
A spokesperson for British Transport Police said: “Detectives investigating a man in possession of an offensive weapon and a serious public order offence on board a train from Erith to London Bridge have today released these images in connection.
“At around 3pm on Monday 23 September, a man slashed several train seats with a knife, including the headrest behind a seated passenger.
“Officers believe the man in the images may have information which could help with their investigation.”
