New York City's COVID-19 test positivity rate on a seven-day average went down to 8.4 percent, compared with 8.44 percent one day earlier, Mayor Bill de Blasio tweeted on Tuesday.

Meanwhile, de Blasio said that there were 230 new hospital admissions and new cases of the coronavirus reached 4,844. "Stay safe and take precautions now as we wait for more vaccine doses to arrive."

"New York City has now vaccinated more people than the entire population of Portland, Oregon. We could be doing MUCH more," said the mayor in another tweet.

"We only have 7,710 first doses left. We need more supplies and we need the freedom to use the 72,409 second doses we have on hand and yet to be scheduled," he added.

While appearing on MSNBC's Morning Joe on Tuesday, de Blasio said, "They're not making enough (vaccine doses). And again, I think it means bringing other pharmaceutical companies into this. Even if it isn't their own brand or patent, we got to break down those silos. This is war. Every company that could be helping to produce vaccines should under federal orders."

"Some of the vaccine has gone to places that absolutely need it, but just don't have the ability to distribute as quickly, and you know, dish the ball to whoever's got the hot hand, to use the basketball analogy, right? If someplace can do it really fast, get the vaccines there first, backfill for the other places," he said.

About the second doses, the mayor said, "If you're sitting on top of, as I am, 100,000 second doses I'm not allowed to use, even though no one can possibly use them for weeks, that doesn't make sense. Let's cut through that, get those into play right away."

As of Monday evening, coronavirus deaths added up to 26,648 and confirmed cases 566,421 in NYC, according to The City, a project that tracks the spread of confirmed COVID-19 infections and fatalities in New York City, based on information provided by the New York City Department of Health and Mental Hygiene, the governor's office, The COVID Tracking Project and the Center for Systems Science and Engineering at Johns Hopkins University.