Alex Salmond has rejected suggestions that an independent Scotland would allow the UK to keep Trident missiles on the Clyde in the same way as its forces have bases in Cyprus.

In an interview on BBC1's Andrew Marr Show, the first minister said Friday's decision by the Scottish National party (SNP) conference to remove Trident from Scottish soil, while still seeking membership of Nato, was non-negotiable.

Ideally, he said, all the UK's nuclear weapons would be scrapped if Scotland won independence. "Far better it was curtains for Trident, I would say," he said.

Salmond and the party's leadership won a very narrow conference vote on Friday to join Nato – reversing a decades-long SNP policy – after an at times ill-tempered and intense debate.

The SNP would now make joining Nato conditional on the alliance accepting that an independent Scotland would require theremoval of Trident nuclear weapons from the Clyde – a measure some critics suggest could cost up to £25bn. It would also insist onparticipating only in military action sanctioned by the UN.

Significant doubts remain on whether an independent Scotland would be allowed to join Nato on those terms. Military experts believe it would have to apply as a new member state, and the MoD believes any application would be rejected if it insisted on removing Trident.

Asked whether it was hypocritical to use Nato's "nuclear shield" while at the same time rejecting Trident, Salmond said: "Nobody seriously believes that Scotland, a country of 5.25 million people, would want to be in possession of nuclear weapons. That would be a bad thing for Scotland. I think that would be a bad thing for nuclear proliferation around the world."

Salmond said a large majority of Scottish voters were opposed to Trident and nuclear weapons. The SNP's own polling, however, shows greater ambivalence among voters on whether a Scottish or UK government has the authority to scrap it.

The latest SNP-commissioned poll asked: "Do you think that the Scottish parliament should have more powers so that it can bring about the removal of Trident nuclear weapons from Scottish waters?" It found 46% of voters in favour and 35% against.

Salmond said that if London was not willing to build a new Trident base within the UK, it had two options: either move the missiles to a US or French submarine base, or scrap the weapons system entirely.

"They could decide on what would be a much better policy, which would be to decommission the weapons system. That would be a matter for the London government," Salmond said.

"That doesn't mean we are going to find it amenable to lease out part of Scottish territory in a Cyprus situation. Scotland by majority doesn't want nuclear weapons. The SNP proposal would be to write that into the constitution of the state and that would make nuclear weapons illegal in Scotland."

Asked about joining the EU while refusing to join the euro, Salmond was careful not to claim an independent Scotland would automatically join and said its entry would be negotiated – but as friends and as part of an existing member.

He said: "We would be negotiating our position within the context of the EU – there's no doubt about that." Because Scotland was already part of a non-euro member state, it would not be forced to join the euro at the same time, he said.

Salmond acknowledged that the yes campaign still faced a significant task in winning popular support for independence. Last week, a series of polls showed a widening gap between support for a yes vote and those who would vote no, with support for separation at about 30%.

That trend was bucked by a new Panelbase poll for the Sunday Times, which put support for independence at 37% against 45% for remaining in the UK. The poll showed that support for independence surged sharply to 52%, 12 points ahead of staying in the UK, if voters thought the Tories would win the next UK general election in 2015.

Salmond said: "Does that mean the yes side is going to win absolutely, definitely? No, but it means it's game on, but there's some substantial indication over the last few weeks that the momentum lies with the Yes Scotland campaign."