SARAJEVO Nov 18 (Reuters) - An Austrian fund offered on Friday to buy the rest of Bosnian holding firm Fabrika Duhana Sarajevo (FDS) for 64.3 million Bosnian marka ($35 million) as part of a plan by British American Tobacco to acquire the firm's tobacco assets.

CID Adriatic Investments (CID) bought a 39.9 percent stake in FDS for 42.7 million marka in September from a Bosnian regional government, using financing provided by BAT.

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CID has now bid for the remaining 60.1 percent stake in FDS, owned by local subsidiaries of Austria's Raiffeisen Bank and Italy's UniCredit SpA, as well as investment funds and small shareholders. FDS has banking and real estate operations, as well as tobacco interests.

The fund said on Friday it had bid 83.5 marka a share for the remainder of the company, the same price as in September and again using BAT financing.

BAT said in September it would enter into exclusive negotiations for the potential purchase of FDS tobacco assets once CID's takeover offer was successfully completed.

An official involved in the deal said then that the transaction had been structured so that BAT would not need to buy FDS's non-tobacco assets.

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FDS's shares were trading at 81.50 marka on Friday, up 4.47 percent from Thursday's close. The shares have risen by nearly a quarter since CID's purchase of the regional government's stake in FDS. The company has a market capitalisation of 100.5 million marka.

The takeover offer is valid for 28 days, CID said. ($1 = 1.825 Bosnian marka) (Reporting by Maja Zuvela; Editing by Daria Sito-Sucic and Adrian Croft)