MILAN, June 7 (Reuters) - Italian insurer Cattolica said on Monday it had decided to delay a planned 200 million euro ($244 million) cash call to give its shareholders the chance to take up a buyout offer by bigger peer Assicurazioni Generali.

Generali, Italy's largest insurer, last week said it would spend up to 1.17 billion euros to buy out investors in Cattolica with a view to taking full control of the rival and delist its shares from the Milan bourse.

Generali's offer is conditional on a postponement of the rights issue, which Cattolica needs to carry out to complete an overall 500 million euro capital strengthening demanded by industry supervisors.

Generali first ran to Cattolica's rescue last year, subscribing to an initial 300 million euro cash call in return for a 24% stake.

Cattolica said it did not want to deprive its shareholders of the possibility to sell out to Generali, by rendering the offer ineffective through the completion of the proposed capital increase.

"This decision does not preclude or condition in any way the right and duty of the board of directors to evaluate the offer and the fairness of the consideration proposed by Assicurazioni Generali," Cattolica said in a statement.

Generali is expected to launch its offer in the autumn once it has received all the necessary authorisations. ($1 = 0.8201 euros) (Reporting by Valentina Za)