All other terms and conditions of the offer remain unchanged, Basel-based Roche said in a statement.
Illumina has already adopted a poison pill defence strategy for Roche's unsolicited of $44.50 per share bid. It told shareholders not to tender any of their shares to Roche, saying the offer failed to properly value its existing and coming products.
The San Diego-based firm makes machines that decode a person's entire genome, going far beyond simple genetic tests that are already used in diseases such as cancer to test for a handful of gene variations.
A deal would give Roche's diagnostics unit a leading position in the market for gene sequencing, which can help better identify which patients benefit from a given drug.
Analysts say Roche, which has a history of success with such hostile takeouts, may have to raise its bid to around $60 per share to win Illumina.
Earlier acquisitions, such as that of diagnostic test-maker Ventana or U.S. biotech group Genentech, show Roche is happy to take its time with deals and that it will ultimately prevail with a sweetened offer.
Roche took seven months to buy Ventana for $3.4 billion in 2008, when Chief Executive Severin Schwan was head of its diagnostics unit. It first made an unsolicited, low-end bid before increasing its original offer by 19 percent.
Roche's offer for Illumina was due to expire on February 24.
(Reporting by Catherine Bosley. Editing by Jane Merriman)