Analysis released by the Treasury argued that leaving would cause "an immediate and profound economic shock" to Britain and damage economic growth.
"With exactly one month to go to the referendum, the British people must ask themselves this question: can we knowingly vote for a recession?" Osborne said in an accompanying statement.
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Osborne and Prime Minister David Cameron have made dire predictions of the effect of a so-called Brexit as they campaign for Britain to remain in the EU.
Osborne's campaign has announced that house prices would fall and grocery prices rise, while the Bank of England governor Mark Carney and the International Monetary Fund have warned of negative consequences for the British economy.
The Vote Leave campaign has accused the other side of scare tactics.
Iain Duncan Smith, a senior member of Cameron's Conservative party who campaigns in favour of Brexit, dismissed the Treasury's analysis as "not an honest assessment".
"The Treasury has consistently got its predictions wrong in the past. This Treasury document is not an honest assessment but a deeply biased view of the future and it should not be believed by anyone," Duncan Smith said.
Opinion polls suggest that the "Remain" camp is likely to prevail.
An average of the last six polls by research project What UK Thinks gives "Remain" an eight-point lead over the "Leave" camp, on 54% versus 46%.
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