The U.S. will get less than half of Gilead Sciences Inc.'s worldwide donation of 1.5 million vials of its COVID-19 medicine over the next six weeks, which isn't expected to be enough to treat all the patients who would qualify for it.

Gilead is donating about 607,000 vials of its remdesivir in the U.S. during that time frame. That's enough to treat 78,000 hospitalized patients, according to the Department of Health and Human Services. Health officials authorized emergency use of the treatment earlier this month.

"Initial supply of remdesivir is likely to be constrained to an even greater degree than we had previously estimated," RBC analyst Brian Abrahams wrote in a note to clients. He said he had been expecting 80% of Gilead's donation to be distributed in the U.S. With less than 50,000 going out in the first two shipments, the rollout was also slower than what he was expecting.

More than 300,000 eligible patients in the U.S. won't have access to the Foster City, California-based company's treatment through the end of July. That and "continued limited supply through almost the end of the year" could put pressure on state health departments, according to Abrahams.

Gilead didn't immediately respond to requests for comment. It's shares rose as much as 2% Monday and have climbed more than 20% this year.

New York State has been at the center of the pandemic with more the 330,000 of the 1.3 million cases of COVID-19 in the U.S. according to Johns Hopkins University data. The state received the largest donation so far when an initial 565 vials were delivered last week as part of an initial allocation to the first seven states, HHS said a statement on Saturday.

In New York, Mayor Bill de Blasio said the amount of the drug shipped to his city was about 10% of what it needs.

"We're still the epicenter of this crisis. So, I am hoping that the White House will hear our plea and quickly get us the additional doses we need," the mayor said during his daily briefing on Sunday.

The agency said that starting on the evening of May 7, six more states would get shipments. That included 30 cases each for Maryland and Connecticut while Michigan would get 40. Hotspots like Illinois and New Jersey would get more at 140 and 110 cases each. Iowa is set to get 10 of the cases, each of which contain 40 vials of remdesivir.

The shortage could bode well for another emergency use approval, this one for Biocryst Pharmaceuticals Inc.'s antiviral treatment, some Twitter users speculated. The stock rose as much as 15% to the highest in a year on Monday. The small-cap company is testing galidesivir in a placebo-controlled trial in Brazil, the first part of the study will enroll 24 hospitalized COVID-19 patients.