Argos and SURA, along with a host of other Colombian entities, form part of the Andean country's largest conglomerate, Grupo Empresarial Antioqueno (GEA).
Many of GEA's more than 100 companies own significant stakes in one another which, until recently, helped protect the conglomerate's assets from hostile takeovers.
Argos said in a statement on Thursday Grupo Gilinski's offer price of $8.01 for each SURA share - which would make the transaction worth over $1 billion - is "considerably inferior" to the fundamental value of the company.
"The price ... does not recognize the fundamental value of its operating companies nor that of its portfolio of investments," Argos said, citing a study by JP Morgan.
Argos will take actions to maximize shareholder value in Grupo SURA and close the gap between its fundamental value and that which is reflected in the market, it said.
Measures will include supporting SURA disclose its value, such as by forming partnerships or listing on international stock markets, as well as boosting profitability, Argos said.
Grupo Gilinski launched a public acquisition offer for up to 62.625% of shares in Nutresa - another GEA company - in a bid worth some $2.2 billion in November, with the backing of Abu Dhabi's Royal Group.
Just weeks later, Grupo Gilinksi shocked the market again by making its move on SURA, the jewel in the GEA's crown. SURA owns 20% to 50% stakes in many of the conglomerates' other companies.
(Reporting by Oliver Griffin; Editing by Alexandra Hudson)