GlaxoSmithKline (NYSE: GSK)may extend its hostile $2.6 billion takeover offer for Human Genome Sciences Inc. a second time to win investor backing for control of the U.S. biotechnology company.

Meanwhile, GSK learned on Thursday that its legal travails over the diabetes drug Avandia are far from over. The drug giant must face a lawsuit from Humana Inc. over costs linked to injuries from the drug.

Shareholders of Human Genome, whose board rejected Glaxo’s $13-a-share bid in May, have until 5 p.m. New York time today to tender their stock, the London-based drugmaker said three weeks ago. Glaxo will probably announce results of the tender offer before the U.S. stock market opens July 2, Navid Malik, an analyst at Cenkos Securities Plc in London, said Thursday.

Human Genome (Nasdaq: HGSI) stock has traded above the offer price since Glaxo proposed the takeover on May 9, signaling that shareholders expect a higher bid. Glaxo extended the deadline to today from June 7 after receiving acceptances from investors owning 0.2 percent of outstanding Human Genome shares. Investors may be holding out as Rockville, Maryland-based Human Genome has said it will accept other acquisition offers through July 16.

“I’d be skeptical if shareholders are ready to tender now, especially ahead of Human Genome completing its process of finding a higher price,” said Brian Skorney, an analyst at Brean Murray Carret & Co. in New York.

Glaxo, the U.K.’s biggest drugmaker which maintains its U.S. headquarters in Research Triangle Park, N.C., is likely to extend the bid deadline and may even raise what it’s offering as it’s committed to the acquisition to gain control of Benlysta, a treatment for lupus, as well as albiglutide for diabetes and darapladib for heart disease, said Fabian Wenner, an analyst at Kepler Capital Markets in Zurich.

The drugmakers cooperate on all three treatments. Glaxo made the hostile offer in May after Human Genome’s board rejected an unsolicited bid in April for the same amount.

“Glaxo doesn’t want to step away from the deal,” Wenner said in a phone interview. “I definitely expect an extension, and potentially a slight improvement in price.”

Avandia Trial

A federal appeals court ruled against GSK in the Avandia suit, reversing a lower- court decision dismissing the complaint.

U.S. law allows so-called Medicare advantage organizations such as Humana’s medical plan and insurance units to sue in federal court to seek such reimbursement, the U.S. Court of Appeals in Philadelphia ruled Thursday.

The language of the Medicare Secondary Payer Act “is broad and unrestricted and therefore allows any private plaintiff with standing to bring an action,” the three-judge appeals panel said in its decision.

Humana, based in Louisville, Kentucky, filed a proposed class-action complaint in November 2010 seeking reimbursement for the costs of treating enrollees in its Medicare advantage program for Avandia-related injuries. About 1 million people are covered by the plan, according to court documents.

Glaxo, which has begun settling claims brought by thousands of Avandia users over various injuries, hasn’t yet included reimbursement of Medicare advantage plans in its settlement agreements, the appeals panel said in its ruling.

“Glaxo respectfully disagrees with the court’s decision and we’re reviewing our options,” Bernadette King, a spokeswoman for London-based Glaxo, said in a phone interview.

Glaxo said in 2010 that it would stop promoting Avandia worldwide after studies linked the drug to increased risk of heart attacks. The company has resolved more than 50,000 lawsuits over the drug.