The petition, which was supported by 2,220 people, urged the government to ensure a stronger enforcement of the law to prevent sales to those underage and illicit trade, and to make proxy purchasing illegal, rather than imposing a costly and damaging ban on display.
However, the government has refused to change its stance.
The Prime Minister's Office said it would still be seeking to remove display of tobacco products at the point of sale "in order to protect children and young people".
It added that it would work with trade bodies to provide support and ample lead-in time for compliance to minimise burdens on business.
Regulations are set to come into force from October 2011 for larger shops, and 2013 for smaller businesses.