The offer - now extended until July 20 - remains pitched at $13 per share.
The decision by Britain's biggest drugmaker to push back the closing date comes as no surprise, since Human Genome effectively extended the battle two weeks ago by setting a July 16 deadline for definitive takeover offers.
In the wake of the GSK extension, Human Genome repeated its rejection of the offer as not reflecting the inherent value of the company.
Buying Human Genome would give GSK the full rights to drugs on which the two companies collaborate.
GSK said on Friday it remained willing to talk to Human Genome, adding: "Extension of the tender offer to 20 July will provide HGS shareholders the opportunity to evaluate the outcome of the HGS board's process relative to GSK's offer.
"Based on circumstances at that time, GSK will consider all available options regarding its offer but can make no assurance that the tender offer will be further extended."
The only company to have made an offer, GSK has consistently refused to participate in the auction process being run by Human Genome's advisers Goldman Sachs and Credit Suisse .
Human Genome says it has had contact with other companies, but bankers say GSK has a big advantage over rivals because of its partnerships around key drugs.
The two companies together sell Benlysta, a new drug for the autoimmune condition lupus, and collaborate on two other experimental drugs for diabetes and heart disease that could become significant sellers.
GSK and Human Genome share rights to Benlysta, while GSK owns the majority of the commercial upside to the other products.
GSK's tender had been due to expire at 9 p.m on June 29. It was first extended on June 8 after GSK secured less than 1 percent of the biotech group's stock in an initial tender round. The latest extension expires on July 20 at 9 p.m.
(Additional reporting by Ben Hirschler; Editing by Matthew Tostevin and David Hulmes)
