Michael Gove has told BBC 1's Andrew Marr Show: "I think it's wrong to claim that this government if favouring one group of individuals over another in public appointments."
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Politicians approved the bill that renames the country North Macedonia, with 69 votes in favour in the 120-member parliament.
The business boss received a backlash for his original message.
Brian John Carron was arrested over the seizure of ammunition and weapons in 2011.