The comments appear to be a significant shift of policy away from decades of the SNP actively campaigning for nuclear disarmament.
However, Alyn Smith later attempted to clarify his comments, stating he and the party stood by their commitment to sign the Treaty on the Prohibition of Nuclear Weapons (TPNW).
The TPNW, which came into force in January last year, prohibits any nation party to it to use, develop or stockpile nuclear weapons.
Ms Sturgeon, speaking just prior to the treaty coming into effect, said she “strongly support[s] the principles” of the treaty, adding an independent Scotland would be a “keen signatory”.
The SNP leader’s opposition to nuclear weapons is central to her politics, with the First Minister stating she joined the Scottish arm of the Campaign for Nuclear Disarmament (CND) a year before joining the party she now leads.
However, comments from the party’s Westminster foreign affairs spokesperson Alyn Smith suggest the SNP may consider ditching its pledge to become a signatory to gain membership of Nato.
No country is both a member of Nato and a signatory of the TPNW.
Mr Smith, speaking at an pro-independence conference in Aberdeen at the weekend, said a “piece of paper isnae going to keep us safe”, while referencing the treaty.
He said: “We're having the issues about signing the TPNW and there are issues with that for us, because the nuclear element of Nato is part of the Acquis Communautaire and that needs to be signed up to.
"But a piece of paper isnae going to keep us safe.
"What [Russian president] Vladimir Putin has done in Ukraine is I think brought home to an awful lot of people in the Yes movement and wider that what is going to keep us safe is international solidarity and a rules-based international order, defended by a credible organisation.
"Does it make me happy, does it give me a warm fuzzy feeling? No it doesnae, but it is a big, cold, chilly world out there and I think we owe it to the people of Scotland that we've done this stuff seriously, we've done our homework on this."
The comments appear to be part of a significant shift away from the SNP’s historical opposition to the Trident nuclear deterrent and pledges to remove the weapons from Faslane.
In the SNP’s manifesto for the Holyrood elections in 2021, the party promises money “spent on Scotland’s priorities – not nuclear weapons” if Scotland becomes independent
It also states: “We will maintain our firm and unequivocal opposition to nuclear weapons – both in principle and to their location in Scotland.
"We want to see a world free from nuclear weapons and an independent Scotland will be a strong and principled advocate for nuclear disarmament on the global scale.”
Donald Cameron, the Scottish Conservative constitution spokesperson, said the comments may have “unmasked” future SNP U-turns.
He said: “The SNP’s stance on Nato and a nuclear deterrent has been inconsistent, confused and completely irresponsible.
“This has been pointed out to the nationalists over many years, and it’s no surprise to see the cracks in policy beginning to show.
“Either the penny has finally dropped with Alyn Smith or he’s accidentally unmasked future SNP policy U-turns, but this latest development again exposes the SNP’s naivety when it comes to serious international affairs.”
The SNP were asked whether the comments meant a change in policy and whether an independent Scotland would still sign the TPNW.
Mr Smith said that he stood by his and his party’s commitment to sign the TPNW.
He said: “The SNP’s commitment to sign the TPNW and remove nuclear weapons from Scotland swiftly and safely has been affirmed not only by conference, but by each individual parliamentarian. This is a commitment I stand by.
“I want an independent Scotland to be able to stand up and face the difficult geopolitical questions of our age.
"There are parties in governing coalitions all over Nato states, including the German Greens, who support the treaty, and do not see it coming into conflict with their support of Nato membership.
“However, treaties amount to little more than ink on a page unless they are actively enforced – the horrors of genocide in Rwanda and the use of chemical weapons on civilians in Syria are testament to that.
"The signing of the TPNW would not be the end of the campaign against nuclear weapons. It would be one milestone on a long journey to create the conditions for a nuclear free world.”