STOCKHOLM, June 21 (Reuters) - Sweden's parliament on Tuesday approved a proposal by the government to allow loss-making airline SAS to convert debt borrowed from the state into equity, as part of a process to help rescue the carrier from collapse.

Fighting to survive, SAS, which is part-owned by Sweden and Denmark, plans comprehensive reorganisation to slash costs, raise 9.5 billion Swedish crowns ($942 million) in cash from owners and investors, and convert 20 billion of debt to equity.

The Swedish government this month suggested parliament agree to the debt conversion, but said no to injecting more cash than it already has into the long-struggling airline.

The Danish government has said it is willing to write off debt and inject more capital however - as long as private investors get on board too. ($1 = 10.0887 Swedish crowns) (Reporting by Anna Ringstrom, editing by Terje Solsvik)