In his second letter to Illumina shareholders this week, Icahn wrote the "only path forward is for Grail to be divested".

Illumina said on Monday it will divest Grail, which it purchased in 2021, if it loses its appeal to the European Commission where regulators said last year they intend to require Illumina to unwind the $7.1 billion takeover.

The company did not have an immediate comment on Icahn's latest letter.

Icahn, who owns 1.4% of Illumina, launched a proxy fight earlier this week and is seeking three board seats at the company after weeks of private discussions with Illumina sputtered.

"We don't believe that it is possible for Illumina shareholders to receive the full value of GRAIL if Illumina pursues both the appeals process and the divestment process at the same time," Icahn wrote.

Illumina won its case against the U.S. Federal Trade Commission which had tried to argue the deal should not go ahead for antitrust reasons.

Icahn's push at Illumina could become the year's most high-profile proxy contest after Nelson Peltz ended his quest for a seat at Disney and Daniel Loeb reached an agreement with Bath & Body Works. A handful of activist investors are still pressuring Salesforce to make changes.

(Reporting by Bhanvi Satija in Bengaluru and Svea Herbst in Rhode Island; Editing by Shounak Dasgupta)