Argos and SURA refused to participate in two previous public offers, saying the values offered by Gilinski - one of Colombia's richest men who is the owner of bank GNB Sudameris and now SURA's largest shareholder - are too low.

The series of offers have shaken up the country's largest conglomerate, Grupo Empresarial Antioqueno (GEA), of which SURA, Argos and Nutresa are members, leaving GEA with limited options to combat Gilinski's efforts.

"Taking into account the technical and strategic analysis presented by J.P. Morgan and other advisors, among other considerations, the board of directors of Grupo Argos decided not to participate in the public acquisition offer for either Grupo SURA or Grupo Nutresa," Argos said in a statement to the country's financial regulator.

Argos said it will continue to work with the companies to maximize value for shareholders.

SURA said in a separate statement that shareholders decided at an extraordinary meeting not to authorize five of its board members, including Gilinski's son Gabriel, to decide on the third offer for Nutresa because they had expressed potential conflicts of interest.

"Based on this decision made by the shareholders, the board of directors of Grupo SURA does not have the necessary quorum to deliberate and decide, exclusively, on the third Tender Offer made for shares in Grupo Nutresa," the statement said.

(Reporting by Julia Symmes Cobb; Editing by Leslie Adler)