Two shareholder advisory firms have recommended that Illumina shareholders reject Roche's offer, and Illumina had said the new offer remained insufficient.
Shortly after Roche's Wednesday morning announcement, Illumina said shareholders at its annual meeting elected Illumina nominees to its board and rejected several Roche proposals, including one to increase the board's size.
"We are pleased that Roche has decided not to extend its inadequate offer to acquire Illumina and that we can now return our full focus to growing our business, making the most of the expanding opportunities in our space, and delivering superior results for our customers and stockholders," Illumina CEO Jay T. Flatley said in a statement from the company.
Illumina makes instruments for genetic analysis. Roche's product portfolio includes the blockbuster cancer drug Avastin. It is the world's sixth largest drugmaker based on revenue, according to the data firm IMS Health.
Roche said its increased offer represented an 88 percent premium over Illumina's closing stock price on Dec. 21, which was the day before market rumors about a potential deal between the companies drove those shares significantly higher.
CEO Severin Schwan had said last week it still believed that the $51 per-share price was fair based on available public information. But he added that "if Illumina were to engage with us, we would consider any information supporting Illumina's contention that our offer undervalues the company and its prospects."
The Swiss company said Wednesday it will keep looking for ways expand its diagnostics business.
Shares of Illumina fell 4 percent, or $1.74, to $42.26 Wednesday morning while broader trading indexes rose more than 1 percent. U.S.-traded shares of Roche climbed 51 cents to $44.57.