Roche's revised offer for San Diego-based Illumina is $6.5 billion, or $51 a share.
The company said in a letter to Illumina that the bid represents a 15 percent premium to its first offer, on Jan. 25, and is 88 percent above Illumina's closing price on Dec. 21, 2011, the day before rumors of the takeover surfaced.
The all-cash offer also represents 34.1 times the multiple of Illumina's projected earnings in 2012.
Roche said it prefers to negotiate a friendly takeover offer with Illumina. However, if the target's management continues to rebuff negotiations, the Basel-based suitor threatened to effect a transaction unilaterally.
Illumina, advised shareholders to defer responding to Roche's latest offer. The company said it intends to review the unsolicited bid thoroughly and make a recommendation in due course.
Illumina, which has a 60 percent market share in next-generation gene sequencing, or decoding, and makes instruments responsible for over 90 percent of all sequencing output, has said it's positioned to deliver more value to shareholders than what Roche's first bid price implies.
The company said it is in an industry on the verge of tremendous growth.
Acquring Illumina and its gene-sequencing technologies would enable Roche to expand its offering of personalized medicines, Dow Jones Newswires reported.
Shares of Illumina were trading Thursday up 4 percent to $51.86. Roche shares fell 1.2 percent to €138.80 ($184.20).