The federal government is increasing the weekly allotment of COVID-19 vaccines to Washington and other states by 16% for the coming weeks, Gov. Jay Inslee announced Tuesday.

News of the increase came during a call between governors and President Joe Biden’s vaccine team, Inslee said in a news conference.

“This is really great news that in such short order the Biden administration has been able to increase the supply,” said the governor, who also touted increases in vaccinations across Washington in recent days.

On Tuesday, the Biden administration announced a plan to purchase an additional 200 million doses of vaccine along with its announcement of increased distribution to states next week.

The development comes after state officials last week expanded eligibility for the vaccine to people age 65 and over.

The decision created a flood of hospital visits and phone calls from people seeking vaccination appointments. On Monday, people struggled to get through to the state Department of Health’s (DOH) own pandemic hotline because of the high volume of calls. In a tweet Tuesday, the department said it had added more capacity and staffing.

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Given the disconnect right now between supply and demand, the coming weeks are likely to include plenty of disappointment for those seeking vaccinations.

More than 1.5 million state residents — out of Washington’s 7.65 million people —are currently eligible for the vaccine, according to the state Department of Health. Meanwhile, Washington has been receiving around 100,000 doses per week from the federal government, Inslee said.

As of Monday afternoon, the state had reported 1,352 new coronavirus cases and 19 new deaths (new data isn’t reported on Sundays so Monday counts may be high).

Inslee on Tuesday also said the state will be receiving higher-efficiency syringes with the next vaccine shipment that can pull an extra dose out of the vials.

“Instead of five doses a vial, we will have six,” said Inslee.

Early on in the distribution, Washington state struggled to quickly get vaccines into the arms of vulnerable people: health care workers and long-term care residents.

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And Washington falls on the lower end of the 50 states and Washington, D.C. for how many residents have gotten at least one shot so far, according to data compiled by The New York Times.

Alaska leads, where 11% of residents have gotten at least one dose of the vaccine, according to that data, with West Virginia at 9.4% and New Mexico at 8.2%. About 5.5% of Washington residents have gotten at least one shot, compared to 6.2% in Oregon.

But Inslee Tuesday touted recent progress on vaccines distribution, saying the daily number of vaccines given out across the state has recently increased.

The state administered about 39,000 doses on Monday, the governor said.

Overall, about a half-million doses have been administered in Washington so far. That sum includes both first and second doses, according to Michele Roberts, an acting assistant secretary with the Department of Health.