David Cameron has pledged that the Tories will back plans to give Scotland more tax and law-making powers, stepping up the battle to win over undecided voters before September's independence referendum.

The prime minister said that increasing the Scottish parliament's powers to raise and set taxes was "the right thing to do" and would not be a consolation prize for Alex Salmond's nationalist government in the event of a no vote in September.

In a move to help build a united platform in favour of greater devolution from all three UK parties, Cameron told the Scottish Tories it was a "blatant" nationalist myth that a no vote would mean the end of the road for further powers.

"Let me be absolutely clear: a vote for no is not a vote for no change.

"We are committed to making devolution work better still, giving the Scottish parliament greater responsibility for raising more of the money it spends," Cameron told the party's spring conference, which has attracted a record number of 1,100 delegates.

"So here's the recap: vote yes – that is total separation. Vote no – that can mean further devolution; more power to the Scottish people and their parliament, but with the crucial insurance policy that comes with being part of our UK."

Cameron's pledge lacked any detail but is designed to further clarify the options facing Scottish voters in September's independence referendum, with the Liberal Democrats and Labour producing blueprints to give Holyrood greater control over income tax rates and other minor taxes.

Blair Jenkins, chief executive of the Yes Scotland pro-independence campaign, leapt on Cameron's use of the word "can" in his speech as evidence of the Tories' half-hearted and "vague" promises. "We now know this is a sham," Jenkins said.

Tory officials rejected that, insisting that Cameron used the word to mean "will" and was wholly committed to further tax powers.

This represents a significant softening of Tory attitudes to further devolution. The Scottish Tory leader, Ruth Davidson, was elected in 2011 after describing new powers to allow Holyrood to modify the UK rate of income tax by up to 10p from 2016 as a "line in the sand".

But with opinion polls repeatedly showing that a majority of Scotland's voters want more powers than those offered in the Scotland Act, the Tories are considering more independence on income tax as part of a closely-guarded review by Lord Strathclyde, the former leader of the House of Lords, due to be published in May.

Scottish Labour's leader, Johann Lamont, is due to publish its devolution commission plans next week. The party is expected to propose a Scottish-run income tax system, which has been endorsed by Gordon Brown, and control over other minor taxes and benefits.

In a speech designed to make a positive case for the UK, Cameron cited his own Scottish roots – a Scottish great-great-uncle served in the first world war – adding that the recent Winter Olympics and this summer's Commonwealth Games in Glasgow gave fresh evidence of the strength of the union.

The Scottish skipper of the UK curling team, Eve Muirhead, had said that representing Team GB was a "great, great feeling" and more than a quarter of volunteers for the Commonwealth Games were coming from outside Scotland.

"It is a great feeling," Cameron said. "It's not about subjection or colonialism or dry pragmatism. It's about being part of a bigger team. A family of nations."

With Scottish police helping English forces during the 2011 riots, or Scottish patients routinely using English hospitals, these parts of the UK were not parts of a foreign country.

While the nations were sometimes argumentative, "we're there for each other", Cameron said. "And let's not forget how unique and precious that is. When you look around the world, so often, tragically, neighbourliness has been lost and replaced by wars and feuds. We don't do that. We don't slam doors and turn compatriots into foreigners."

Cameron added that recent warnings from banks such as Lloyds and RBS, and from firms such as BP and Shell proved that the economic and financial risks of independence were not bluff and bluster or bullying.

He cited warnings from José Manuel Barroso, the outgoing president of the European commission, that an independent Scotland would find it very hard to smoothly join the EU. "These are not political puppets, they are serious, non-partisan figures," he said.

"So the idea that these are empty warnings and political scaremongering is a myth – and we owe it to the people of Scotland to take that myth apart."

Nicola Sturgeon, the Scottish deputy first minister, said Cameron's promises were "half-hearted, vague suggestions of what might happen", and that Cameron's reluctance to commit to anything "spoke volumes".

"Indeed, the only reason the Tories are even talking about more powers is to attempt to bribe the people of Scotland into voting no – but it is unravelling fast," she said. "The no camp is clearly getting increasingly rattled, as recent polls show more and more people are moving to yes."