June 11 (Reuters) - The CEO of gene-sequencing machine maker Illumina Francis DeSouza has resigned from the group, it said on Sunday, weeks after he survived a challenge to his board seat from activist investor Carl Icahn.

In May Icahn secured a seat for one of his three nominees to Illumina's board, marking a partial victory for him and his months-long proxy battle to remove DeSouza.

The company said on Sunday senior vice president and General Counsel Charles Dadswell will take over as interim CEO while a replacement for DeSouza is found. DeSouza will stay on in an advisory capacity until July 31, it added.

DeSouza survived the challenge to his board seat from Icahn last month by securing more than twice the number of shareholder votes than his challenger received.

Icahn has been a vocal critic of the company's $7.1 billion acquisition of cancer diagnostic test maker Grail.

Illumina earlier this month filed an appeal against an order from the U.S. Federal Trade Commission (FTC) that demanded it divest Grail on competition concerns.

(Reporting by Lavanya Ahire in Bengaluru; Editing by Jason Neely and Jan Harvey)