Conservative leader David Cameron has warned the SNP not to "obstruct" a replacement for the Trident missile system if his party wins the next election.
But his argument was rejected by Scotland's First Minister Alex Salmond who said Holyrood was entitled to make known its views by every available means.
The clash came in a television documentary to be screened on Sunday night marking 10 years of devolution.
Britain's Trident nuclear missile submarines are based at Faslane on the Clyde but the SNP argues that nuclear weapons should not be based in Scotland.
In 2008 it set up an anti-Trident working group, saying there was broad support in Scotland for this stance.
Mr Cameron, who is most likely to win the next General Election, told the programme that defence was a UK issue and Conservatives supported Britain having an independent nuclear deterrent.
The Leader of the Opposition said: "This is important and that's a mandate if we're elected that we will have to deliver.
"I respect the ability of the Scottish minister and the Scottish Parliament to say, right, on tuition fees, or prescription drugs or whatever, we take a different view.
"But likewise the argument does go the other way - that if a Government in Westminster has a mandate to deliver issues to do with nuclear deterrence or the size of the army or whatever, then they should be able to do that without the Scottish Government trying to obstruct them."
But Mr Salmond said his party would campaign against a Trident replacement "at every available opportunity".
The First Minister said: "I don't see how there could be a complaint about the government of Scotland or the parliament of Scotland seeking to use its own powers to advance a point of view.”
And it was "perfectly legitimate" for Holyrood to use the powers available to it to influence what happened in Scotland, he went on.
Mr Salmond added: "If that missile system is unwanted by the body politic of Scotland, unwanted by Scottish members of parliament at Westminster, not wanted by the Scottish Parliament, then surely that Prime Minister would expect the Scottish Parliament to make its view known in every area and way that was open to it to do.
"I think that is a perfectly legitimate thing to do.
"The idea that you can base a new generation of nuclear missiles in Scotland, and not talk or listen to the people of Scotland about it is ridiculous."
Mr Cameron has pledged to treat Scotland with "respect" if he becomes Prime Minister. On Saturday, it was revealed he had conceded the Conservative Party was wrong to oppose devolution.
