The robbery happened on Sunday, August 5, at around 5.20pm at Nilus Mini Market on Livesey Branch Road, Blackburn, when four men have gone to the store, but only three went inside.
A police spokesman said: "One of the trio has produced an axe and made demands for money to a woman working in the shop.
"The other two then walked behind the counter and took a quantity of cigarettes.
"The man with the axe tried to open the till but was unsuccessful."
The offenders were then chased from the shop.
DC Rhiannon Cosgrove from East CID said: “It is important that we trace these men and so if you think you know who they are or you have any information at all that could help our investigation, please get in touch.”
You can contact police at lancashire.police.uk/reportonline or can call East CID on 01282 472523 quoting crime number ED1817917. If you fail to get an answer you can ring 101.
Alternatively independent charity Crimestoppers can be contacted on 0800 555111 or online at crimestoppers-uk.org.
A 17-year-old-boy from Blackburn was arrested in relation to this incident and has been released under investigation pending further enquiries.