BOGOTA, Feb 24 (Reuters) - Colombia investment holding company Grupo SURA said on Thursday its board has unanimously decided not to participate in a second public acquisition offer for shares in food producer Nutresa by business magnate Jaime Gilinski.

Gilinski's conglomerate, Grupo Gilinski, has launched four public acquisition offers for shares in Nutresa and SURA itself.

Both companies are part of Grupo Empresarial Antioqueno, or GEA, a sprawling conglomerate of more than 100 firms. Many of GEA's companies own large portions of each other's shares.

Gilinski - one of Colombia's richest men and the owner of bank GNB Sudameris - has shaken up the tightly interwoven holdings with the offers, with Grupo Argos and SURA declining to participate in the first offers because they believed the price offered by Gilinski underestimated their value.

Grupo Argos said late on Tuesday it also would not participate in the second offers, again because it considers the price to be too low.

"The Board of Directors of Grupo SURA unanimously decided not to accept the second tender offer for Grupo Nutresa shares," SURA said in a statement to the country's financial regulator.

"An eventual acceptance of this bid would disregard relevant aspects for Grupo SURA and its shareholders," it said, listing concerns about Nutresa's value.

The board "considers inappropriate the messages of those who suggest that the only right decision would be to accept the tender offer under the conditions offered," it added.

Gilinski told Reuters this week his acquisition offers for Nutresa and SURA could help other GEA companies raise funds to invest in their businesses and reduce debt, as he redoubled his efforts to convince shareholders to sell. (Reporting by Julia Symmes Cobb Editing by Marguerita Choy)