It also asks the Government to tackle the discrepancies between the punishments for drugs smuggling and tobacco smuggling offences and bring the penalties for illicit tobacco crime in line with those for drugs offences.
The petition needs to generate 100,000 signatures for the Government to debate it in Parliament.
But it currently stands at just 122, so it needs to attract another 99,878 signatures before the deadline of March 19.
In a bid to drum up support for the petition, Peter Nelson, Imperial Tobacco’s anti-illicit trade manager, said: “Selling counterfeit or illegally smuggled tobacco is not a victimless crime and it impacts on society in many different ways.
“Community spirit is eroded with the intimidating presence of criminals operating on our streets threatening the livelihoods of legitimate retailers and the reputation of famous tobacco brands.
“The renowned quality of brands with a long and distinguished history is being undermined as counterfeit products expose consumers to brands which are not manufactured to the extremely high standards to which genuine brands are and do not comply with all regulatory requirements.
“Another consequence is that successful age verification campaigns such as No iD No Sale and Citizencard become meaningless in an illegal environment as the criminals directly target children when peddling their illicit tobacco.
“Their activities cost the average convenience store over £30,000 per year in lost sales (IGD research 2012 & MS Intelligence Empty Pack Survey 2012) – equating to over 4,000 lost tobacco purchases, to say nothing of the lost impulse purchases from other categories generated by tobacco.”
To sign the e-petition visit http://epetitions.direct.gov.uk/petitions/43213