* Cevian stake now 12-15 pct - source
* Wants supervisory board representation
* Thyssen shares up 1.2 pct, outperform Dax (Adds more on Cevian stake, source)
FRANKFURT, Jan 27 (Reuters) - Swedish activist investor Cevian has increased its stake in German steelmaker ThyssenKrupp to between 12 and 15 percent, a financial source familiar with the matter said on Monday.
Cevian is also seeking representation on the supervisory board to reflect its shareholding but does not plan to change the composition of the management board, Thyssen said in a statement filed to the stock exchange on Monday.
ThyssenKrupp, once a symbol of Germany's industrial prowess, has been trying to shift its focus from the volatile steel sector to higher-margin products and services such as elevators, industrial plants and high-performance car parts.
Cevian had increased its stake last month to about 11 percent as part of a capital increase at Thyssen and according to Monday's statement from Thyssen, one of Cevian's funds had a 10.06 percent share of the voting rights as of Jan. 24.
Thyssen shares were up 0.8 percent by 1135 GMT, while Germany's benchmark DAX was down 0.4 percent.