(Reuters) -Proxy adviser Glass Lewis said on Wednesday Illumina Inc shareholders should vote for two of Carl Icahn's nominees to the firm's board, as representatives who can challenge the current board would be beneficial to the company.

Glass Lewis added shareholders should vote against the re-election of the current chief Francis deSouza and chair John Thompson, saying they had enough reasons to advocate for a new chair.

The recommendations come ahead of the company's annual shareholder meeting on May 25, which could bring to an end the two-month long proxy battle between Illumina and billionaire investor Carl Icahn.

Icahn, who owns 1.4% of Illumina, began a boardroom battle at the gene sequencing company in March. He has called for Illumina, now valued at around $31 billion, to unwind its deal for Grail, which he said was a risky and costly acquisition that cost shareholders $50 billion.

Separately, Icahn's investment firm Icahn Enterprises LP is fielding enquiries from U.S. prosecutors about its operations after short-seller Hindenburg Research accused the firm of over-valuing its assets.

Glass Lewis said in a report it recommends shareholders support Icahn's nominees, Vincent Intrieri and Andrew Teno, adding the company's $7.1 billion acquisition of cancer-testing firm Grail had been a "costly, distracting, value-crimping millstone" for Illumina.

The proxy adviser also said Illumina investors should hold the current management directly accountable for the several risks and uncertainties surrounding the company's "questionable determination" to close the Grail deal, without regulatory approval.

However, it did not extend support to Icahn's third candidate, Jesse Lynn, adding that election of all three candidates was not needed.

Illumina did not immediately respond to a Reuters request for comment.

Shares of the company rose over 5.7% to $205.3 following the report.

(Reporting by Bhanvi Satija in Bengaluru; Editing by Krishna Chandra Eluri)