Swiss drugmaker Roche Holding AG, in a letter to Illumina Inc shareholders, called its sweetened $51-a-share offer for the maker of genetic analysis equipment a more than reasonable starting point for negotiations.

The latest salvo in Roche's repeatedly rebuffed efforts to buy Illumina comes a week ahead of Illumina's shareholder meeting and suggests Roche is willing to raise its offer.

Illumina shares have been trading above $51 and closed at $52.57 on Nasdaq on Wednesday.

The letter from Roche Chief Executive Severin Schwan urged Illumina shareholders to vote for Roche's proposed slate of director nominees and its other proposals at next Wednesday's meeting in New York and laid out the case for the $51 per share offer that amounts to about $6.8 billion.

It calls the offer a significant premium to where Illumina would likely trade on a standalone basis and a very attractive one but adds the phrase a more than reasonable starting point for negotiations.

Despite the appearance of a willingness to further sweeten an offer that began at $44.50 per share, Schwan characterizes the future of an independent Illumina as far from certain amid increasing headwinds for Illumina and the broader sequencing sector.

The Roche CEO goes on to ridicule Illumina's own letter to shareholders in which it said it had been called the Apple of the genomics business. He said Illumina's gene sequencing products were not the iPhone and the iPad, referring to Apple's popular personal electronics products.

Illumina's products on the other hand, although 'revered by genomics researchers around the world,' serve a much smaller and highly regulated market. And unlike at Apple stores, crowd control of eager buyers has not been a problem for Illumina, the Roche letter said.

Illumina declined to comment on the Roche letter.

Roche's efforts to get its slate of directors elected to the Illumina board look to be a longshot after three proxy advisory firms have recommended that shareholders back Illumina's nominees.

Illumina has urged its shareholders not to tender shares to Roche and to reject the larger company's nominees.

(Reporting By Bill Berkrot in New York; Editing by Gunna Dickson and Tim Dobbyn)