Gabrielle Giffords, the former Arizona congresswoman who survived being shot in the head during a mass shooting in 2011, has launched an organisation promote new restrictions on gun ownership and to take on the powerful National Rifle Association.

The move by Giffords, who has become a leading voice of the gun control movement in America, comes at a time of increased pressure on the gun lobby in the wake of the horrific Newtown school shooting at the end of last year.

Giffords, together with her ex-astronaut husband, Mark Kelly, are now promoting their new group, which is called Americans for Responsible Solutions, and asking for donations to fund its efforts.

In an editorial published in the USA Today newspaper on Tuesday morning the pair pointed out that since the attack on Giffords in Arizona exactly two years ago there have been 11 further mass shooting in the US and yet no legislative action has been taken. "When it comes to protecting our communities from gun violence, we're not even trying," they said in the column.

Giffords also launched an attack on the gun lobby which is spearheaded by the powerful NRA. Giffords described the organisation's response to the Newtown massacre – which consisted of a suggestion that school shootings could be prevented by having armed staff – as "defiant and unsympathetic".

Her new group is aiming to provide a counter-balance to the immense lobbying power of the NRA by raising funds that it can then use to back politicians who advocate greater gun control. "Until now, the gun lobby's political contributions, advertising and lobbying have dwarfed spending from anti-gun violence groups. No longer. With Americans for Responsible Solutions engaging millions of people about ways to reduce gun violence and funding political activity nationwide, legislators will no longer have reason to fear the gun lobby," the column stated.

Giffords is likely to be a powerful force for gun control. The story of her recovery from grievous injuries has made her a well-known and inspiring figure for many Americans. She has already visited Newtown to speak with the families of some of the 20 children and six adults who died in the massacre by a lone gunman at the town's Sandy Hook elementary school.

However, few details of exactly what sort of gun controls ARS will push for have yet emerged. Both Giffords and Kelly have been at pains to stress that they support the right to bear arms in the US and indeed are both gun-owners themselves. Instead they are calling for people to get in touch with ARS to "join a national conversation about gun violence prevention".

Nor is Giffords alone in seeking to shape that debate from a position of pushing for new gun controls. The group Mayors Against Illegal Guns released a new TV advert on Tuesday featuring Roxanna Green, whose nine-year-old daughter, Christina-Taylor Green was killed in the same Tucson shooting that Giffords survived. The advert includes a statement from New York mayor Mike Bloomberg, who has also emerged as a leading voice for gun control. "How many more children must die before Washington does something to end our gun violence problem?" Bloomberg says in the advert.

The push by gun control advocates comes as President Barack Obama has given strong hints that he intends to back a push to introduce some form of new law on the issue in the wake of the Newtown tragedy. The White House has said that a task force headed by vice-president Joe Biden will make a report by the end of January on how to proceed with potential new policy proposals.

The Brady Campaign to Prevent Gun Violence estimates that on average some 100,000 Americans are shot and injured or killed with a gun each year. It also says that homicide by firearm rate in the US is almost 20 times higher than most other developed industrial countries despite similar non-lethal crime and violence rates.

No one from the NRA responded to a request for comment by The Guardian.