Scottish Secretary Alistair Carmichael has said the leaking of a memo which claimed Nicola Sturgeon would prefer David Cameron to be prime minister was "just one of those things".

Mr Carmichael confirmed the memo was written in the Scotland Office but denied it was embarrassing for him.

He said: "This is the middle of an election campaign, these things happen."

Ms Sturgeon has said the claims in the memo are "100% untrue".

She was alleged to have told the French ambassador that she would prefer to see the Conservatives remain in power after the 7 May general election.

Cabinet Secretary Sir Jeremy Heywood has ordered an inquiry into how the note got into the public domain.

Mr Carmichael told Channel 4 News: "I understand that the memo in question did actually come from the Scotland Office, but these things are circulated within government."

Meanwhile, chancellor George Osborne has said the UK would have higher debt and taxes and weaker defences if the SNP "propped up a weak Ed Miliband government".

Mr Osborne said it was clear there would be "an unholy alliance" between Labour and the SNP in the election.

He argued that SNP leaders were "much stronger" than Mr Miliband.

Image copyright other Image caption George Osborne warned of higher taxes and debts if Nicola Sturgeon's SNP propped up a Labour government

The SNP said the claims were "simply untrue" while Labour said the SNP and the Tories were "playing political games" with the country's future.

Labour has ruled out any formal coalition with the SNP in the event that the general election results in a hung parliament. But Mr Miliband has stopped short of ruling out a more informal alliance.

On Sunday, Ms Sturgeon renewed her appeal to the Labour leader to work with the SNP in order to "lock David Cameron out of Downing Street" after the 7 May vote.

Speaking to Sky News, Mr Osborne said: "The fact that a Labour party which was a party that campaigned for the United Kingdom in the referendum is contemplating an arrangement with the SNP who want to break up the country is deeply disturbing.

"People know that Ed Miliband is weak, that the Scottish Nationalist leaders are much stronger than he is, and we know who would be running that government.

"That would be bad for the entire United Kingdom, bad for the integrity of the union, but also bad for our economy because it would mean higher debts and higher taxes."

Asked if Labour could form an anti-austerity alliance with the SNP, Labour's Treasury spokesman Chris Leslie told Sky News: "I'm not sure quite what the SNP are saying - they say one thing in public and another thing, it appears, in minutes.

"I don't know quite what was going on there but I think a lot of people are not surprised at the revelations that perhaps Nicola Sturgeon actually does secretly want a Conservative government.

"Why do they want that? Well, they'd love to get into a second referendum and look at jeopardising the Union in this way.

"The SNP and the Conservatives, I think, are playing political games with our country's future.

"We have ruled out a coalition with the SNP. We don't believe in doing that with them, because they believe in totally different things, in breaking up the United Kingdom. We don't believe in that."

Biggest party

The SNP's general election campaign director Angus Robertson said Mr Osborne's claims were "simply untrue".

He added: "The SNP is putting forward sensible plans for modest spending increases instead of cuts, which would support investment and public services while still reducing the deficit.

"In contrast, all that is on offer from the Tories is tens of billions of pounds worth of further austerity that would do further damage to communities across Scotland."

On Sunday, Ms Sturgeon called on Mr Miliband to work with her party after the general election.

Writing in the Observer newspaper she said: "I repeat my challenge to Ed Miliband - if together our parties have the parliamentary numbers required after 7 May, and regardless of which is the biggest party, will he and Labour join with us in locking David Cameron out of Downing Street?"

Ms Sturgeon's comments came after an inquiry was set up over the leak of a memo claiming she would prefer the Tories to win the election.

Cabinet Secretary Sir Jeremy Heywood ordered the investigation into how the document, published in the Daily Telegraph, got into the public domain.

Ms Sturgeon said the account of a conversation she had with the French ambassador was "100% untrue".

French officials said she had not expressed a preference for prime minister.

Ms Sturgeon has accused Whitehall of "dirty tricks" over the Daily Telegraph story.

Campaign trail

Meanwhile on the election campaign trail, SNP deputy leader Stewart Hosie was in Dundee, urging voters to back his party in order to secure "a fairer future" for families across the UK.

He said: "This election offers Scotland - and the rest of the UK - the chance for change, breaking out of the mould of two and three party politics.

"Last week's seven party leaders' debate showed there is an appetite across the UK for progressive voices to be heard."

In a "State of the Race" memo to Scottish Labour activists, deputy leader Kezia Dugdale said the past week had "demonstrated clearly" the choice on offer at the election.

She also highlighted the reach of Scottish Labour's campaign, adding that the party had already been in touch with every one of the 190,000 voters that leader Jim Murphy committed to contacting in December.

She added: "We've still got over four weeks left, and we need to build on the success we've had so far."

During a visit to Edinburgh, Scottish Secretary Alistair Carmichael claimed working Scots would pay £400 a year more under the SNP's income tax plan than they would under his party, the Liberal Democrats.

He said: "The SNP talk a good game about helping the less advantaged, but they don't have a redistributive policy to their name.

"Here's a chance for Nicola Sturgeon to match the Liberal Democrat promise of an additional £400 tax cut for the less well off. She doesn't want to."