An SNP government whip admitted there could now be a full-blown "rammy" at the party's autumn conference over the issue, which has divided party activists, many of whom are fundamentally opposed to Nato as it is founded upon nuclear weapons.
The row represents the most serious internal challenge to Salmond's authority since he returned as SNP leader in 2004.
The dissent has escalated since mid-July, when MP Angus Robertson, the SNP's leader at Westminster and the party's defence spokesman, said the Nationalists should end their 30-year-old opposition to joining the North Atlantic Treaty Organisation.
He said that if Scotland became independent after the 2014 referendum, it would inherit the UK's membership of Nato, and should maintain it while insisting that Trident be removed from Scotland.
The U-turn is intended to make the party's defence policy more credible ahead of the referendum, as it would silence claims that an independent Scotland would be left unprotected. However, it has alarmed SNP activists who see Nato as synonymous with nuclear weapons.
Other parties have also accused the SNP of being hypocritical in demanding removal of Trident while sheltering under Nato's nuclear umbrella.
Founded in 1949 on the principle of collective defence, Nato's 28 member states agree to defend one another in the event of external attack, with that help extending to the nuclear arsenals of France, the UK and the US.
In order to change party policy, Robertson has tabled a motion to the SNP conference in Perth in October, stating that an independent Scotland would "maintain Nato membership subject to an agreement that Scotland will not host nuclear weapons."
Salmond is supporting the motion.
Last week, in a sign of nervousness within the SNP leadership, the party ordered MSPs not to speak publicly about the issue, and provided them with a stock answer to deflect media enquiries.
But at least half a dozen MSPs are this weekend backing a rival amendment calling for opposition to Nato to continue, while co-operating with other European defence alliances.
It calls for Robertson's Nato membership plan to be deleted and replaced by: "Conference resolves that the SNP position will be that Scotland should not remain a member of Nato".
The amendment is being tabled by Jamie Hepburn, MSP for Cumbernauld and Kilysth, who has previously described Nato as a "destabilising factor in the West's relationship with Russia".
At least five other SNP MSPs have now confirmed they too will oppose Nato membership – John Finnie, Dave Thompson, Jean Urquhart, Sandra White and John Wilson – with around the same number understood to be on the brink of a declaration.
One SNP dissenter said people were worried that giving in over Nato would be the start of a slippery slope, and that the fight was ultimately about the broader culture of the SNP.
"If you give up before you have fought you are New Labour in 10 minutes. A lot of the brighter MSPs recognise that. As soon as the leadership win on Nato, they'll be wanting to keep Trident next."
Urquhart, a Highlands and Islands MSP, said she would be supporting Hepburn's amendment. "My absolute fundamental [objection to Nato] is that I think Scotland could be a world leader in starting a serious nuclear disarmament programme."
Thompson, MSP for Skye, Lochaber and Badenoch, said: "The main problem for me with Nato is that it is a nuclear alliance with a first strike nuclear policy, which is extremely worrying. I think it would also make it much more difficult for us to argue the case for removing Trident from Scotland if we are going to be a Nato member.
"I'm absolutely opposed to nuclear weapons. We should be working much harder to get rid of them."
Central Scotland MSP Wilson said he wanted to remain outside Nato, which was increasingly a military proxy for the US. He told the Sunday Herald: "I continue to support the current party policy on Nato and hope that conference supports that position."
White, MSP for Glasgow Kelvin, said she was "happy" to express her support for the amendment.
And Hepburn said: "I do intend to take forward an amendment and look forward to having a debate."
Glasgow MSPs John Mason and Bob Doris said they would give the amendment serious consideration.
Anniesland MSP Bill Kidd, an SNP whip and a long-term anti-nuclear campaigner, said he "could handle" Nato membership, but admitted there was widespread disagreement and predicted a fiery conference debate.
He said: "I wouldn't be surprised if it got heated because it's a big issue and a longstanding one. People have plenty of time to think up what their arguments are between now and the conference, so we should be able to get a decent debate going rather than just a rammy. I hope so, anyway."
Party MSPs now face weeks of arm-twisting and lobbying in the run-up to the conference vote. Moreover, Trident Ploughshares is planning a protest outside the SNP's Edinburgh HQ this week. And CND has started a letter-writing campaign.
The SNP's CND group will also hold a conference in Glasgow on August 25 to help "counter the attempt by the SNP leadership to change SNP policy from an anti to a pro-Nato stance".
SNP-CND convener Gareth Finn, a member of the Nationalists' ruling executive committee, said: "The overarching theme of the referendum campaign is a positive vision of what can be achieved when the people of Scotland reclaim their independence.
"The proposal to not only commit the SNP to Nato membership but also to lock the SNP in to a range of current Nato policies will undermine the appeal of what can be achieved with independence".
CND demonstrators are expected to picket the SNP conference, urging delegates to vote according to their conscience not the leadership line.
James Kelly, Labour chief whip at Holyrood, said: "Normally, Alex Salmond can command blind allegiance from his followers on the back benches. But the rank and file are becoming increasingly emboldened in criticising his strategy."
A Scottish Conservative spokesman said: "Alex Salmond has been opposed to Nato for three decades and his sudden support for membership has everything to do with the referendum.
"It's not surprising that even his own MSPs have seen through his cynicism."
An SNP spokesman said: "SNP members have the democratic opportunity to make their views on Nato membership clear at conference, where we expect to have an excellent debate on defence policy, including reaffirming the Party's strong anti-nuclear stance."