Tesla CEO Elon Musk said Wednesday on Twitter that the company would make ventilators in case of a shortage during the coronavirus pandemic. Now, New York City Mayor Bill de Blasio is holding his feet to the fire.

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"New York City is buying!" de Blasio tweeted at Musk on Thursday. "Our country is facing a drastic shortage and we need ventilators ASAP — we will need thousands in this city over the next few weeks. We're getting them as fast as we can but we could use your help!"

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Musk later responded, "we will connect with your team to understand potential needs."

A spokesperson for the Mayor's Office told CNBC in a statement they had reached out to Musk's family office and his lobbyist.

"Given his response on Twitter, we're hopeful he will be able to help," the spokesperson said.

But it's unclear what capacity Tesla will have to produce the ventilators.

Two major U.S. automakers, General Motors and Ford, are looking into how their facilities can support the production of medical equipment. That could involve giving up extra space in factories to manufacture ventilators, CNBC previously reported, according to people familiar with a conversation between GM CEO Mary Barra and President Donald Trump on Wednesday. The Big Three U.S. automakers — GM, Ford and Fiat Chrysler — agreed Wednesday to temporarily shut down U.S. factories following worker union pressure.

Tesla is still making new cars at its Fremont, California, plant despite orders from the Alameda County Public Health Department to wind it down to "minimum basic operations" after "shelter-in-place" orders were put in effect on March 17.

Even though the county does not define Tesla's factory as an "essential business," the company is arguing that under federal rules, it should be counted as "National Critical Infrastructure" and therefore remain operational. The Fremont factory makes Tesla Model 3 and Model Y vehicles, which are its most popular electric sedans and newest crossover SUVs, for North America and Europe.