"The first minister has been a Nationalist all his political life," said the Scottish labour leader.
"I'm giving him the opportunity to resolve the issue. Why won't he take it?"
She told MSPs: "I'm not the problem, Labour's not the problem, the legislative timetable's not the problem, even [deputy Scottish first minister] Nicola Sturgeon isn't the problem.
"The first minister is the problem when it comes to resolving this issue in the nation's interest."
But Mr Salmond said the SNP would stick to its manifesto pledge, adding: "This is a serious process, which is why we're engaging with it in a serious way."
He went on: "It is impossible for anyone outside the Labour Party - and I think most people in it - to take the Labour Party seriously after the last few days."
'Boil needs lanced'
The first minister added: "While I would not say Wendy Alexander is the only problem the Labour party has, I think quite convincingly after the last few days that she is not the answer."
As the row dominated question time, Scottish Tory leader Annabel Goldie attacked the "grudge, gripes and grievances" which defined the relationship between Mr Salmond's government and that of Gordon Brown's at Westminster.
"For those millions of people in Scotland who do want devolution to work the Labour Party may have abandoned them but the Conservatives have not," she told parliament.
"A referendum on something so important as the constitutional future of Scotland, a country we all love, cannot be allowed to become a vote on the unpopularity of Gordon Brown and Wendy Alexander - that is an unacceptably dangerous road to take."
Nicol Stephen, the Scottish Liberal Democrat leader, asked: "Can the first minister believe his luck? Over the past year he has seen the Conservatives cosy up to him and back his budget.
Mr Salmond and Ms Alexander went head-to-head over the issue
"They were the best of friends, until this week when the farcical floor show of the modern-day Labour Party came into view. With Labour and Tories like this, does he think life can get any better?"
Outside parliament, the row continued with CBI Scotland director, Iain McMillan, branding the issue a "boil on Scotland's neck that needs lanced".
Mr McMillan, a member of the independent Calman Commission currently reviewing devolution, said the country should move quickly to hold a vote and settle the issue.
Earlier, Labour MSP Malcolm Chisholm came to Ms Alexander's defence, insisting her call was the right one, adding: "She has widespread support not only within the Labour Party but I believe throughout Scotland."
Mr Brown, he added, held the Scottish Labour leader in the highest regard and trusted her political judgement.
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