But analysts say Roche, which has been successful with previous hostile deals, will ultimately have to raise its $44.50 per share bid to win Illumina, whose shares closed at $51.22 on Friday.
Illumina has already adopted a poison pill defence strategy for Roche's unsolicited bid, and has advised shareholders not to tender any of their shares on the grounds the price was too low.
The extension by Roche was expected, Illumina said. An extremely low number of shares have been tendered, consistent with our view - and that of our stockholders - that Roche's offer does not reflect Illumina's unique leadership position, business performance and future prospects.
Only about 0.1 percent of Illumina's shares outstanding have so far been tendered to Roche, the Basel-based firm said .
Roche shares were down 0.6 percent at 0831 GMT, outperforming a 1.1 percent softer sector index <.SXDP>.
Ultimately, we reckon Roche will get Illumina. It may take 6-12 months, and a sweetened offer, analysts at bank Vontobel said. Overall we like the acquisition and believe it will be value-creating once integrated into Roche's network.
Earlier acquisitions such as that of diagnostic test-maker Ventana and 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.
San Diego-based Illumina 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 Basel-based 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.
The offer for Illumina had been due to expire on February 24 and Roche said on Monday all other terms for the offer remained the same.
(Reporting by Catherine Bosley. Editing by Jane Merriman)