Ministers have been urged to "get their finger out" and clamp down on airguns following the death of Andrew Morton.
Andrew Morton died after being shot near his home
Mark Bonini, 27, has been convicted of murdering the two-year-old, who was shot in the head in Glasgow in March.
The Scottish National Party said talks between the Scottish Executive and the Home Office had failed and Holyrood should be given the powers to act.
But the justice minister said her aim was to get "a workable solution" which would prevent a repeat of the tragedy.
Cathy Jamieson said: "That is why I have asked the Home Office and my own officials to examine the possibility of licensing schemes, to examine the possibility of restricting the sale of such weapons and to consider all the possible options.
"That is what we committed to do and we haven't moved. We are still committed to seeing a tightening up of the legislation."
Andrew's death in the Easterhouse area of Glasgow immediately sparked calls for tighter controls of air weapons.
The toddler's mother, Sharon McMillan, is campaigning for the introduction of Andrew's Law - with a complete ban on the weapons.
Speaking outside the High Court on Tuesday, she said that Bonini's conviction would strengthen the family's campaign.
The issue is reserved to Westminster, where the minimum age for owning an airgun was increased from 14 to 17 last year.
Go it alone
In June this year the Home Office unveiled new legislation which would raise that limit to 18 and restrict where the weapons can be fired.
First Minister Jack McConnell said that the proposals did not go far enough and raised the possibility that Scotland could go it alone on the issue.
SNP justice spokesman Kenny MacAskill said the discussions between the executive and the Home Office had been dragging on for months and that action was needed now.
He told the BBC's Good Morning Scotland programme: "The time for negotiation and discussion with Westminster has passed.
"The time for the Scottish Parliament to have the powers has come, and the time for the Lib-Lab executive to actually get their fingers out and take the necessary action is fast upon us."
Mr MacAskill said Westminster had "failed" and that Scotland had a distinctive problem which should be addressed in a distinctive Scottish way.
He added that the continued sale of such weapons in high street shops across the country was "an incitement and an insult to the memory of Andrew Morton".
Sharon McMillan wants airguns to be banned in Scotland
Ms Jamieson said she would be speaking to her Westminster counterpart in the coming days.
While the executive was prepared to take forward a scheme in Scotland, she said she would prefer to bring about some "speedy" changes to the Westminster legislation.
"We have an opportunity there to work with Westminster to get an early result on this and that is what I want to focus on.
"I think we owe that to Andrew Morton and his parents," said the minister.
A Home Office spokesman said: "The government will not hesitate to bring forward whatever further measures it is agreed are necessary."