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Dugdale launched the flagship policy in London last month in a bid to revive Labour's ailing fortunes north of the border, where support for the party has slid to 15%.
She said that while the 1707 Act of Union between Scotland and England still underpins the relationship between the two countries, a new Act was needed for the 21st century.
Her proposals for the new settlement included abolishing the House of Lords to replace it with elected regional senates, and creating a "People's Constitutional Convention" whereby an assembly of citizens makes proposals for the shape of the new political system.
Speaking to BBC Scotland, Corbyn said that he "wouldn't use the words" Dugdale had when she launched the policy. "I want us to look at the constitutional relationships. I wouldn't use the words 'new Act of Union'," he said.
Corbyn expressed support for a constitutional convention, however. He said: "There is a huge issue about regional government across England, and there is a need to have a discussion about the relative powers in Scotland, in Wales and in Northern Ireland of devolved assemblies."
Corbyn's comments come at the end of a difficult week for the Labour party. On Wednesday he attempted to relaunch himself as an insurgent populist candidate, but the day was marred by a series of U-turns and seemingly contradictory statements.
It is also the latest indication of Corbyn's difficult relationship with Dugdale, who has previously been critical of the party leader, and backed Owen Smith in September's leadership contest.
Corbyn did not attend Dugdale's Act of Union policy launch last month, and she admitted that they had not even met on her visit to London.
PoliticsHome also revealed in September that the pair came to blows in a "fiery" meeting of Labour's National Executive Committee just hours after he was re-elected as leader in September.
A spokesperson from Scottish Labour said in a statement: "Kezia Dugdale has proposed a new Act of Union, to strengthen our union across the whole of the UK for generations to come.
"Being part of the UK protects jobs and the money we need to invest in our public services."