The Conservatives are to push for a change in the law that would allow judges to keep Scotland's worst criminals in prison until they die.
The party's leader, Ruth Davidson, said it would introduce a member's bill to Holyrood making the case for the introduction of whole-life sentences.
It comes after the shop owner who murdered schoolgirl Paige Doherty had his sentence reduced by four years.
John Leathem will now serve at least 23 years in prison rather than 27.
Leathem stabbed 15-year-old Paige 61 times after she went to his delicatessen in Clydebank in March.
But appeal court judge Lord Turnbull ruled last week that the original sentence had been "excessive" and "inconsistent with current sentencing practice".
He said that Leathem had been a "family man of previous good character who had not offended before and who had expressed remorse", and ruled that the fact Paige's murder was not premeditated should also have been taken into account.
The Justice for Paige campaign group later described the ruling as "heartbreaking", adding: "She had her whole life ahead of her and it's been ripped apart. In 23 years her killer will walk the streets."
By BBC Scotland political editor Brian Taylor
John Leathem stabbed his schoolgirl victim Paige Doherty 61 times but, according to his lawyers, had shown genuine remorse. His minimum term in prison was reduced from 27 years to 23. Paige's family said there were no words to describe their feelings.
Ruth Davidson found words on their behalf today. She roundly criticised the decision and argued, further, that it merited examination as part of a review of sentencing guidelines and practice.
The First Minister's response was instructive. She could, of course, have opted to duck the question, falling back on the argument that the independence of the judiciary must be defended and protected.
That, she implied, would be the mode Ministerial when dealing with such matters. To be clear, the FM did indeed stress the vital importance of independent courts.
But there was more. Ms Sturgeon added that she was a human being in addition to heading the Scottish government.
In that human role, she contrived to leave the chamber in no doubt that she disagreed profoundly with the judicial verdict. Ms Davidson nodded supportively.
Speaking at First Minister's Questions on Thursday, Ms Davidson argued that it was "entirely unacceptable" that Paige's family had seen her killer's sentence being reduced "simply because he was not as bad of a killer as others".
And she said the law needed to be changed "so that families like Paige Doherty's feel that the law is tipping back in their favour and that the worst criminals are kept off our streets forever".
She added: "As it stands our judges do not have the tool of a whole-life tariff at their disposal, and we say that they should.
"We can sit in this parliament and we can wring our hands and we can express outrage every time something like this happens, or we can do something about it.
"I want to do something about it. If the Scottish government won't act, then I can say today that the Scottish Conservatives will do so by pushing ahead with a member's bill making the case for the introduction of whole-life sentencing in Scotland."
First Minister Nicola Sturgeon, who met Paige's mother last year, said that there were "literally no words to express the pain and grief she and the rest of the family have gone through."
But she added: "This was a decision of an independent judge in a court of law - we have an independent justiciary in this country.
"As well as being first minister I am a human being and there are many occasions where I look at decisions of courts and wish that different decisions had been reached.
"It may well be that this is one such case, but I respect the independence of the justiciary and I don't think anybody in this chamber would expect me to interfere with those decisions."
Ms Sturgeon went on to say that it was "right and proper" that the Sentencing Council should look at the issue in depth, and said the government would seriously consider any proposals for change.
But she said it was not fair to say that families were routinely let down by Scotland's "strong and well-performing" justice system.
And she said there were "no guarantees" that Leathem would have been given a whole-life sentence if the option had been available to the trial judge.
The first minister added: "No matter what framework and context parliament sets on any of these issues, we will still have instances where decisions by courts are decisions that many people feel are the wrong decisions.
"That's in the very nature of an independent judiciary.
"But I am very clear that where there is evidence the law has to be changed or action has to be taken, then that is something this government and this parliament should reflect on very seriously."
Whole-life orders have been given to about 80 killers - including Moors murderers Ian Brady and Myra Hindley - since they were introduced in English courts in 1983.
But in Scotland, judges handing down a life sentence must set a minimum term after which the prisoner will be eligible for parole.