NEW YORK (CBSNewYork) — There’s good news for qualified New Yorkers looking to get vaccinated.

The challenge to secure COVID vaccine appointments is apparently easing up as thousands of spots become available.

READ MORE: Judge Lifts Temporary Pause On Vaccine Mandate For NYC Teachers And Other City Workers, Who Now Must Be Vaccinated By Monday

If you tried getting a vaccine appointment in March, you likely can relate to the frustration of countless people who tried for hours, sometimes days, trying to secure a spot.

Now, it’s taking merely minutes and there are plenty of options, but the fact that the appointments aren’t being filled quickly has some people and local leaders concerned.

COVID VACCINE

Thursday, City Councilman Mark Levine tweeted that there were thousands of appointments still available at the Javits Center.

He wrote, “This is the most popular vaccination center in NYC. Until now [appointments] have often gone in minutes. This is a deeply worrying development.”

He went on to say, “Our challenge is no longer managing the crush of demand. It’s bringing [vaccines] to people who need it, and building trust in this life-saving solution.”

Many people responded, expressing concern that perhaps there’s an increase in vaccine hesitancy after the pause of the Johnson & Johnson vaccine.

CORONAVIRUS PANDEMIC

Mayor Bill de Blasio and the city’s health commissioner, Dr. Dave Chokshi, say the city has been getting more robust supplies of Pfizer and Moderna vaccines, and their increased availability is no reason for alarm.

WATCH: Mayor De Blasio Gives COVID Update

READ MORE: 'I Want A Proper Education': Some NYC Public School Students With Medical Exemptions From In-Person Instruction Feel They're Falling Behind

“Vaccine supply is kind of a week-by-week thing, but we, we have seen that times, including recently, some increases in Moderna and Pfizer, and that’s helpful, particularly with the J&J vaccine on hold right now,” de Blasio said. “You can go online and get an appointment anytime, that’s the ideal. That’s fantastic. Definitely seeing a decline in hesitancy … We think there’s a whole ‘nother wave of people we can now get to.”

“There’s now a longer window … before they get filled, and that’s very important, actually, to ensure that we are reaching the people that we want to reach from with respect to vaccination,” Chokshi said.

Meanwhile, Assemblyman Jeff Dinowitz is upset the city closed a popular walk-in site for the elderly in the northwest Bronx.

“What does this now mean for accessibility of the vaccine in that neighborhood?” CBS2’s Jessica Layton asked.

“I’m not sure what people who are 75-plus are going to do,” Dinowitz said.

The city needs the school space as students return to the classroom, moving the site 3.5 miles to the Edenwald YMCA.

“Which is clear across the Bronx,” Dinowitz said. “Every community in every zip code has to have the opportunity for easy accessibility.”

Now that there are so many appointments available, the city says it will be working on their outreach efforts to make sure that everyone who needs to be vaccinated is vaccinated.

Watch Hazel Sanchez’s report

The U.S. is still averaging about 70,000 new infections a day. Dr. Anthony Fauci says the country needs to be careful about lifting restrictions until daily cases are closer to 10,000.

That prompted a heated exchange with Republican Jim Jordan during a hearing on Capitol Hill.

“What measures have to be attained before Americans get their First Amendment liberties back?” Jordan said.

“I just told you that … We’re not talking about liberties. We’re talking about a pandemic that has killed 560,000 Americans,” Fauci said.

Also Thursday, the CEO of Pfizer said a third booster will likely be needed within 12 months of full vaccination, adding it’s possible people will have to get the COVID vaccine every year, just like the flu shot.

Pfizer hopes to have a booster ready by the fall.

MORE NEWS: MTA To Start Issuing $50 Fines To Riders Not Wearing Masks

CBS2’s Jessica Layton contributed to this report.