New York is set to receive another 5 percent boost in its weekly supply of COVID-19 vaccines from the feds, officials said Tuesday — as the city announced it had administered more than 1 million doses in the Big Apple.

State and local officials have been railing for weeks about the lack of vaccine supply, with the White House slowly increasing the number of doses.

White House officials promised governors in a morning conference Tuesday that they would be increasing the number of weekly doses to states by 5 percent for each of the next three weeks, Gov. Andrew Cuomo later told reporters. 

New York is currently getting about 300,000 doses a week, Cuomo said — leading to just 10 percent of state residents receiving their first shot of the two-dosage regimen in the eight weeks since the program started.

A total of 2.5 million doses have been given out in the state in all, the governor said.

Federal COVID-19 Response Coordinator Jeff Zients defended the Biden administration’s vaccination efforts in a separate virtual briefing with reporters Tuesday.

“When we came into office three weeks ago, the weekly delivery was 8.6 million doses,” Zients said. 

“And today we’re announcing that we will increase weekly vaccine doses going to states, tribes and territories to 11 million,” he said, calling it a more-than 25 percent increase over the past few weeks.

Mayor Bill de Blasio on Tuesday said there have been 1,032,158 COVID-19 shots administered in the Big Apple to date — a figure he had hoped to reach last month. Of that amount, 716,492 were first doses and 222,763 were second.

His wife, First Lady Chirlane McCray, got her shot in the arm Tuesday at Kings County Hospital in Brooklyn. McCray qualified for the immunization because of her age, 66.

Hizzoner blamed state and federal bureaucracy for the lag in local immunizations, as well as drug manufacturers, saying at his own press briefing, “We need to see the pharmaceutical companies set up in a way they are not right now,” noting there are only two immunizations currently available.

Cuomo predicted the shortage would not be substantially alleviated until drug-maker Johnson & Johnson’s one-shot vaccine gets to market. 

“The supply will only increase when and if Johnson & Johnson[‘s vaccine] is approved,” the governor said, adding that there should be news on that front in the next two weeks.

“The Pfizer, Moderna vaccine is ramping up, but the ramp-up is relatively slow,” Cuomo said of the two immunizations currently being used. “So we won’t see a major supply increase from Pfizer and Moderna … nowhere near what we need.”

He added that the feds on Tuesday had said they are “adamantly opposed” to states using second-dose supplies for first doses amid the shortage.

Cuomo said that in the case of people who get first doses but don’t show up for their second shots, the state has to wait 42 days before it can use the immunizations on other people. 

And if someone shows up for their second shot after the 42 days, the state must still come up with that follow-up dose, the governor added. 

The state and the city are still wrestling with racial disparities among those who get the vaccine — prompting a state senate bill demanding that the state Health Department “provide a public vaccination plan detailing the steps being taken to ensure the equitable distribution of a COVID-19 vaccine,” according to a release from its upstate Democratic sponsor, Sen. Tim Kennedy of Buffalo.

The senate Health Committee on Tuesday approved having the entire body vote on the bill.

The developments come as the statewide positive-test rate for the virus Tuesday was 5.12 percent — although New York’s rolling seven-day average has dropped to 4.3 percent, the lowest since Dec. 1, Cuomo said.

New York City’s latest seven-day average is 8.09 percent, de Blasio said.

Long Island still leads the state in terms of regions’ positive-test rates, with 5.36 percent, Cuomo said, while The Bronx is the city’s most troublesome area at 6.8 percent. 

Additional reporting by Aaron Feis