MILAN, Sept 28 (Reuters) - Italian insurer Cattolica's said on Tuesday that its board considers that bigger rival Generali's takeover offer for it is at a fair price.

Generali, Italy's largest insurer, earlier in May said it would launch a 1.17 billion euro buyout offer for smaller rival Cattolica to further strengthen its domestic market leadership.

Generali, which already holds a stake of almost 24% in Cattolica, is offering investors 6.75 euros ($7.91) a share to take full control.

Shares in Cattolica have consistently traded above the bid's price. On Tuesday Cattolica shares were down 0.14% at 7.15 euros.

Generali first moved on Cattolica last year, coming to its rescue with a 300 million euro investment after supervisors told the Verona-based insurer to bolster its finances.

Following the move Generali became the single largest investor in Cattolica, relegating Warren Buffett's Berkshire Hathaway to second place when one excludes a 12.3% holding held by Cattolica itself.

The offer will run from Oct. 4 to Oct. 29. ($1 = 0.8537 euros) (Reporting by Andrea Mandala; additional reporting by Nishit Jogi in Bengaluru; editing by Valentina Za, Jane Merriman and Sandra Maler)