Roche stepped up pressure on Illumina shareholders in its battle to take over the U.S. gene sequencing company, telling them in a letter that its increased $6.7 billion bid represented concrete value in a high-risk market.

The Swiss pharmaceuticals company again appealed directly to Illumina shareholders to accept its bid after the U.S. company's board rejected the offer ahead of its April 18 shareholder meeting.

"Roche's increased offer represents a significant premium to where Illumina would likely trade on a standalone basis and provides certainty of value through an all-cash payment to Illumina's shareholders," Roche said in the letter.

The two firms have been at odds to win over shareholders. A source close to the situation said top Illumina shareholder Capital Research, which owns 11.4% of the company according to Thomson Reuters data, had pressured the board to engage with the Swiss drugmaker after Roche's improved bid.