The move to put pressure on Illumina's board during its upcoming April 18th annual general meeting came after the US group's management rejected the revised offer from Roche of $51 that bettered its original bid of $44.50 by 15 percent.
In its letter to the US firm's shareholders, Roche said that the Illumina board has "continually made a number of qualitative statements regarding the potentially large market for its products in emerging markets and industrial end-markets."
"However, the company has yet to produce any quantifiable evidence or projections to reassure shareholders when or how this growth will be realised," it asserted.
"Tender your shares into our offer and vote for Roche's independent director nominees and other proposals at the 2012 Illumina annual meeting," appealed Roche.
The Basel-based pharma giant first launched its bid for Illumina on January 25th.
But the US provider of integrated systems for DNA sequencing had opposed the hostile move saying Roche's offer price was too low and "does not reflect Illumina's unique leadership position, business performance and future prospects."
As a result, take up of the previous offer had been minimal. On March 26th, Roche said it had received shares worth just about $6.4 million.
The Swiss group therefore raised its offer on March 29th, which was rebuffed by Illumina's board on April 2nd.