Washington (CNN) The governor of the state hardest hit by the coronavirus pandemic is calling on the federal government to nationalize the effort to acquire medical supplies at a time when state leaders say they've been forced to compete with one another for the desperately needed equipment.

"I think the federal government should order factories to manufacture masks, gowns, ventilators, the essential medical equipment that is going to make the difference between life and death," New York Gov. Andrew Cuomo said during a news conference Sunday in Albany, New York. "It's not hard to make a mask or PPE (Personal Protective Equipment) equipment or a gown, but you need companies to do it."

The comments from Cuomo come as hospitals continue to sound the alarm on quickly dwindling medical supply stockpiles needed to treat patients as the number of Covid-19 cases surge around the country. State governments have faced having to buy medical supplies -- like masks, gowns and swabs -- themselves or wait for the federal government to fulfill requests submitted for more items. That response, governors say, has so far met a fraction of states' needs.

Federal Emergency Management Agency Administrator Peter Gaynor said in an interview earlier Sunday on CNN that if state officials find needed items on the market, they should purchase them and the agency would pay them back later

"The demand on these critical items is not only nationally, it's globally," Gaynor said. "So, we've been shipping. We shipped today, we're going to ship tomorrow. We're linking supplies, not only from the national stockpile, but from vendors and commercial donations."

But Cuomo, a Democrat, said that because state officials have had to procure the medical supplies needed to treat patients, each state is essentially in competition with one another for the items.

"Currently, when states are doing it, we are competing against other states. In some ways we're savaging other states. I'm trying to buy masks. I'm competing with California and Illinois and Florida," he said, adding that price gouging has become "a tremendous problem."

Illinois Gov. J.B Pritzker likened the situation to the "wild west," telling CNN's Jake Tapper Sunday that "this should have been a coordinated effort by the federal government."

"We're competing against each other. We're competing against other countries. You know, it's a wild west, I would say, out there. And indeed, we're overpaying, I would say, for (personal protective equipment), because of that competition," Pritzker, a Democrat, said on "State of the Union."

But as governors expressed concern, President Donald Trump appeared to signal a different message on Sunday about the coordination between states and the federal government, writing in a tweet, "Working very well with States and our Nation's Governors. #TEAMWORK."

He then responded to Pritzker and other governors directly, saying in a later tweet that they "shouldn't be blaming the Federal Government for their own shortcomings. We are there to back you up should you fail, and always will be!"

The burden to acquire supplies has been placed on governors and state officials, with Trump saying last week that they should work with private companies to secure masks and other items. Days later, the President said the federal government had procured millions of masks and would be distributing them directly to the states, but officials so far have not provided details on the specific supplies or amounts sent.

Trump has also repeatedly said he's using his authority under the Defense Production Act to ramp up production of medical supplies needed to combat the virus, but has not yet wielded those federal powers.

The 1950s legislation provides the President with a broad set of powers to require businesses to "prioritize and accept government contracts" as well as "provide economic incentives" to ensure the US has the stockpiles it needs to handle an impending medical crisis.

The White House has put FEMA in charge of coordinating the federal response, but Pritzker and New Jersey Gov. Phil Murphy have said that the agency has only fulfilled a portion of the requests they've sent.

"We need more (personal protective equipment) both to protect our healthcare workers and to treat the sick," Murphy, a Democrat, said in an interview Sunday on ABC.

Pritzker told CNN that his state still needs more items so he's "got people on the phones, working the phones, calling across the world, frankly, to get this stuff shipped to Illinois."

Companies begin manufacturing supplies

To help combat shortages, a number of companies in the US and abroad have publicly pledged their support

Trump said in a tweet on Sunday that Ford, General Motors and Tesla were given a "go ahead" to make ventilators and other metal products "FAST."

"Go for it auto execs, lets see how good you are?" he wrote of the car manufacturers.

Following the tweet, a spokesperson at Ford said, "We are moving fast to address these efforts and will provide more information when we have it."

GM spokesman Jim Cain told CNN that "the work we announced Friday continues." Last week, the company announced that it would work in coordination with a ventilator company to help increase production.

CNN has reached out to Tesla for comment.

Hanes has also said it was asked by the Department of Health and Human Services if the company was capable of making the type of cotton face masks officials envisioned. The company confirmed it could and voluntarily converted its manufacturing capability to do it.

Hanes spokesman Matt Hall said in a statement that the company will not be making the much-needed N-95 masks , but rather "3-ply all-cotton face masks that are washable and reusable and were developed in conjunction with HHS for use when N95 masks are not required or are unavailable."

Hall said the federal government will handle distribution of the masks.

As of Sunday afternoon, there are at least 31,019 known cases of the novel coronavirus in the US and more than 380 deaths caused by the virus, according to a tally by CNN.

This story has been updated with additional developments Sunday.