President Donald Trump on Sunday criticized Illinois Gov. J.B. Pritzker and "a very small group" of other governors for "blaming" his administration "for their own shortcomings."

".@JBPritzker, Governor of Illinois, and a very small group of certain other Governors, together with Fake News @CNN & Concast (MSDNC), shouldn't be blaming the Federal Government for their own shortcomings," Trump tweeted. "We are there to back you up should you fail, and always will be!"

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Pritzker responded to Trump on Twitter soon after, saying, "You wasted precious months when you could've taken action to protect Americans & Illinoisans.

"You should be leading a national response instead of throwing tantrums from the back seat," he added. "Where were the tests when we needed them? Where's the PPE? Get off Twitter & do your job."

"I want to thank the many public servants in the military, in @fema & other parts of the fed. government who are actually doing the work to keep people safe," he added. "My staff and I are grateful for your experience and your willingness to act courageously on behalf of your fellow American."

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The Trump administration has come under criticism for its production and distribution of testing kits of essential hospital items, like masks and ventilators, to the states. The administration has insisted that it has ramped up production of testing kits and has gotten private industry to increase the manufacturing of such items. Sunday afternoon, 3M announced that more than "500,000 respirators are on the way to two of the more critically impacted areas, New York and Seattle, with arrivals expected starting tomorrow."

Governors, leading Democrats and hospitals have implored the administration to use the Defense Production Act to increase the capacity to produce needed equipment. The 1950 law allows the president to mobilize businesses to fulfill orders deemed necessary for the national defense, in addition to other measures. Trump authorized the law last week but has yet to use it.

Federal Emergency Management Agency Administrator Pete Gaynor on Sunday threw cold water on hopes that the federal government will use the law.

"Yeah, so I think it's an insurance policy," Gaynor said on NBC News' "Meet the Press. "It's a lever. If we have to throw that lever, we will. And it's pretty amazing. You know, companies from around the country volunteering to do all sorts of different things to help Americans. And so we haven't had to use it yet.

"Will we have to use it? Maybe. But right now, this is what makes America so great — every company pitching in making sure we can beat this virus. And so it's been really great to see."

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He added that if governors can find masks "on the open market, go buy it," because "FEMA will reimburse you."

Speaking at the White House coronavirus task force press conference later Sunday, top White House aide Peter Navarro said, "We're getting what we need without putting the heavy hand of government down."

Pressed further on it, Trump said, "We're a country not based on nationalizing our business" and pointed to Venezuela.

Responding to Gaynor's remarks, former Vice President Joe Biden, the Democratic presidential front-runner, said in a statement that Trump "is still failing."

"Mr. President, stop lying and start acting," Biden added. "Use the full extent of your authorities, now, to ensure that we are producing all essential goods and delivering them where they need to go. President Trump's dithering on preparing us for this global pandemic and his lies about his response to this dangerous crisis is one of the most unjustifiable failures of presidential leadership in American history."

Speaking on CNN's "State of the Union," Pritzker said the federal government's response to the crisis has improved since earlier this month but that Illinois has gotten only about a quarter of the personal protective equipment it has requested from the Trump administration.

"We ... got a call this morning, before I went on the air, that we're going to receive another shipment of PPE later today or tomorrow from FEMA," he said. "But it's a fraction still of what we have requested. We need millions of masks and hundreds of thousands of gowns and gloves and the rest. And, unfortunately, we're getting still just a fraction of that."

Pritzker said that, as a result, his state has to compete on the open market — against other states — for those items. Trump has pushed for states to secure masks and other essential items on their own.

"We're all competing against each other. This should have been a coordinated effort by the federal government," he said. "And the national defense authorization that the president has to essentially push this manufacturing really hasn't gone into effect in any way. And, so, yes, we're competing against each other. We're competing against other countries. It's a ... Wild West, I would say, out there. And, indeed, we're overpaying, I would say, for PPE because of that competition."

Pritzker echoed other governors who spoke Sunday. Maryland Gov. Larry Hogan, a Republican, said the lack of protective equipment "is a problem that everyone's been talking about for a week."

"We pushed for action, and we are getting progress," Hogan said. "Now, it's not nearly enough, it's not fast enough, we're way behind the curve, but ... we're trying to figure out what to do moving forward. They are making progress, it's not fast enough, but on all of those things, on respirators, on PPEs, on the masks, on the tests, we're ramping up."

Hogan added that "failures were made and things should've happened sooner."

"But I just want to focus on where we go from here, because our job is to save the citizens," he said.

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On ABC News' "This Week," New Jersey Gov. Phil Murphy said the state is "desperate for more PPE equipment, personal protective equipment."

"We've had a big ask into the strategic stockpile in the White House," he said. "They've given us a fraction of our ask. We are, as a state, private sector, public sector, nonprofits turning over every stone, but we need a lot more PPE, both to protect our health care workers and to treat the sick."

Also on "This Week," Michigan Gov. Gretchen Whitmer said her biggest issue remains not having enough test kits, saying her state needs better data to make important decisions moving forward.

"We're all building the airplane as we fly it right now," she said. "We're doing the best that we can. We're going to continue to be aggressive, and we're continually monitoring what the next move we can make is.

"But we need the federal government to get us those test kits. We need PPEs, as Phil was just saying, we need clear, directive and — guidance from the federal government," she said. "And frankly, a patchwork strategy of each state doing what they can is — we're going to do it if we have to, but it would be nice to have a national strategy."

Whitmer added: "We've got to have those masks."

"Had the federal government really started focusing when it became clear that the whole world was going to be confronting this, we would be in a stronger position right now," she said, adding, "I can't afford to have a fight with the White House, but the fact of the matter is at some point we are going to have to analyze where all the failures were. ... Lives will be lost because we weren't prepared."