Delyn Labour MP David Hanson told MPs that 13-year-old George Atkinson had died when a pellet hit his head after an airgun went off accidentally.
Mr Hanson said the law should require airguns to be stored in metal gun cabinets, with trigger locks for the weapons further improving safety.
Policing Minister Brandon Lewis said he would consider the suggestions.
The teenager, from Pontblyddyn in Wales, near Mold, was playing with another boy when an air gun accidentally went off.
Mr Hanson said that the pain of that loss remained strong for the family and they wanted further tragedies to be prevented.
He said that in the last 27 years, 17 children had died as a result of airguns.
"Sadly the circumstances of George's death could be repeated today unless further action is taken," Mr Hanson said.
The MP also said that the RSPCA had reported a 49% increase in airgun attacks on animals over two years, and the charity wanted the legal age for unsupervised use of airguns to be raised from 14 to 17.
Mr Hanson said that securely locking away airguns in a metal gun cabinet when not in use, as with other firearms, would be a "small but important change" which would deter young people.
Requiring trigger locks on the weapons would further improve safety, he added.
Responding for the UK Government, Mr Lewis said that public safety was the top of his agenda, but that it was important to strike the right balance.
He said everyone had to take responsibility to ensure that weapons are not handled unsupervised by those under the age of 18.
"What is reasonable can and will vary according to the circumstances," Mr Lewis said.
The minister said the UK government recognised that there were legitimate uses for air weapons, such as shooting sports, but confirmed he would look again at Mr Hanson's ideas.
In Scotland it will be a criminal offence to have an air weapon without a licence or permit from 31 December 2016.
The events which led to a child's death from an airgun shot in 1999 could happen again, a Welsh MP has warned.