Police released CCTV images in a bid to catch the vandals responsible for the attack on the Lions of the Great War memorial which they say has caused a significant amount of distress in Smethwick.
The statue was defaced just days before Remembrance Sunday with the phrase 'Sepoys no more', while a black line was drawn through the words 'Great War'.
Sepoy was a term given to troops in the British Indian Army.
West Midlands Police said the vandalism was being treated as racially-aggravated criminal damage.
The 10ft-high statue, which is between High Street and Tollhouse Way and was only unveiled on November 4, was targeted just five days later, leaving a community sickened.
Superintendent Martin Hurcomb, from the Sandwell Police, said: “Officers are working closely with the congregation and management at the nearby Guru Nanak Sikh Temple as we understand that this attack has caused a lot of concern in the community.
“Work continues to try to understand the reasons behind what happened and identify whoever is responsible. I’d urge anyone who recognises the people in this CCTV to get in touch as soon as possible.
“Local officers continue to work closely with communities and have increased police presence in the area to provide reassurance and be on hand to answer any questions or concerns that people may have.”
The statue is the first of its kind marking 100 years since the end of the First World War and commemorating the millions of men from the British Indian Army who served in both world wars.
Hundreds of people attended the unveiling on Smethwick's High Street just a week before Remembrance Sunday.
Police have appealed to anyone who recognises the people in the images or has information about what happened they can contact us via Live Chat at west-midlands.police.uk between 8am to midnight, call 101 anytime or contact Crimestoppers anonymously on 0800 555 111.