The coalition of more than 30 state attorneys general called on the government to act or allow states to do so, saying in a letter to US health agencies that Gilead "has not established a reasonable price" for remdesivir.
"Gilead should not profit from the pandemic and it should be pushed to do more to help more people," the letter said.
The drugmaker is charging most US patients $3,120 per course, or $520 per vial of remdesivir.
The medicine is one of only two that have demonstrated an ability to help hospitalized COVID-19 patients in formal clinical trials. It received emergency use authorization (EUA) in the United States and approval in other countries after it shortened hospital stays in a large US trial.
In the letter, the coalition, led by Louisiana Attorney General Jeff Landry and California Attorney General Xavier Becerra, urged Remdesivir the federal government to exercise its rights under the Bayh-Dole Act and license remdesivir to third-party manufacturers to scale up production.
The letter went to the heads of the US Health and Human Services (HHS) department, the National Institutes of Health, and the Food and Drug Administration.
Gilead and the health agencies did not immediately respond to requests for comment.
The US government, which provided some financial backing for the drug's development, signed a deal with Gilead in June for more than 500,000 courses of the treatment, making up most of the company's output through September.
Gilead agreed to send nearly all of its remdesivir supply to the United States between July and September, according to HHS. The agency and states are managing allocation of the drug to U.S. hospitals over that period.
The government said it would receive around 94,000 treatment courses in July, 175,000 in August, and another 233,000 in September.
Still, the drug has been in scarce supply since the US EUA in May, and hospital staffers and politicians have complained about difficulties getting access to it.
"Shipments are coordinated by the federal (government) and we have a bad disconnect between what they think we need and what we really need," US Senator Marco Rubio of Florida tweeted last month, before announcing further allocation to his hard-hit state.
Over the past four weeks, just under half of the US remdesivir supply has gone to COVID-19 hotspots Florida, Texas, California and Arizona.
Gilead has teamed up with generic drugmakers based in India and Pakistan, including Cipla Ltd and Hetero Labs Ltd, to make and supply remdesivir in 127 developing countries. But only limited production has begun.
Last month, Cipla priced its generic version of remdesivir at $53.34 per 100 milligram vial, roughly one-tenth of the US price.