A chorus of Republican and Democratic governors pushed back hard after United States President Donald Trump accused Democrats of playing "a very dangerous political game" by insisting there is a shortage of tests for the coronavirus. The governors countered that the White House must do more to help states do the testing that's needed before they can ease up on stay-at-home orders.

Kansas Democratic Governor Laura Kelly said the current federal effort "really is not good enough if we're going to be able to start to open our economy. We cannot do that safely without the tests in place."

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Supply shortages have stymied US testing for weeks. The needs range from basic supplies like swabs and protective gear to highly specialised laboratory chemicals needed to analyse patient results.

Hospitals, laboratories and state health departments report scouring the globe to secure orders, competing against each other and their peers abroad.

The governors' plea for stepped-up coordination came on Monday when the Trump administration again provided discordant messaging: Trump blasted state leaders on Twitter for being too dependent on the federal government and said later that some governors just did not understand what they had, while Vice President Mike Pence assured governors the government was working around the clock to help them ramp up testing.

Vice President Mike Pence, centre, and Health and Human Services Secretary Alex Azar during a tour of the secretary's operations centre [Andrew Harnik/AP Photo]

Pence sought to soften the administration's message amid growing clamour from both parties for a national testing strategy to help secure testing swabs, chemical reagents and other crucial supplies.

"When it comes to testing, we're here to help," Pence told governors during a video conference from the headquarters of the Federal Emergency Management Agency (FEMA). The Associated Press news agency obtained audio of the call.

Pence said the administration sent each state a detailed list Monday of testing capacity.

But Maryland Republican Governor Larry Hogan said much of the unused lab machinery listed for his state was in federal labs to which the state does not have access. Pence said the administration has agreed to open up federal labs to help states.

Hogan announced Monday that the state had received 500,000 tests from South Korea - a "game-changing" deal negotiated by his wife, Yumi Hogan, who grew up outside Seoul.

"They want the states to take the lead, and we have to go out and do it ourselves, and so that's exactly what we did," Hogan said.

Trump didn't take that lying down. In his daily briefing, he said some governors have "more capacity than they understand".

"The governor of Maryland could have called Mike Pence, could have saved a lot of money," Trump said. "I don't think he needed to go to South Korea. He needed to get a little knowledge."

In Ohio, Republican Governor Mike DeWine said his state is working with another federal agency, the US Food and Drug Administration, to find a source of reagent, the chemical used to analyse test results.

"A lot of good things are going on, but we're not there yet," DeWine said.

Democratic Montana Governor Steve Bullock said his state received 5,000 nasal swabs Monday from FEMA - evidence the federal government is listening. But he added, "It doesn't get us far enough."

In New York, Democratic Governor Andrew Cuomo said the states should take the lead on testing but it's up to the federal government to help sort out supply-chain issues facing testing manufacturers.

"What the states will run into is when you talk to those labs ... they buy machines and equipment from national manufacturers," said Cuomo, who met Trump at the White House on Tuesday. "And those labs can only run as many tests as the national manufacturers provide them chemicals, reagents and lab kits."

Pennsylvania Democratic Governor Tom Wolf said, "We need the reagents, we need the test kits and I think that's the sort of general cry from other states."

As Pence spoke with the governors on Monday, Trump took to Twitter with a more combative tone than his vice president, complaining that the "radical left" and "Do Nothing Democrats" were playing politics with their complaints about a lack of tests.

"Now they scream ....'Testing, Testing, Testing,' again playing a very dangerous political game," Trump tweeted. "States, not the Federal Government, should be doing the Testing - But we will work with the Governors and get it done."

... "Testing, Testing, Testing," again playing a very dangerous political game. States, not the Federal Government, should be doing the Testing - But we will work with the Governors and get it done. This is easy compared to the fast production of thousands of complex Ventilators! — Donald J. Trump (@realDonaldTrump) April 20, 2020

Public health experts say the country needs to dramatically increase its testing infrastructure if it is going to safely roll back restrictions and reopen businesses without risking a major spike in infections.

Dr Anthony Fauci, the nation's top infectious diseases expert at the National Institutes of Health, told ABC's Good Morning America on Monday that the country is currently running about 1.5 million to 2 million tests per week. But, he said, "We really need to get up to, at least, you know, maybe two times that, three times that."

The White House said the Pentagon is finalising negotiations with a Maine medical company to ramp up production of nasal swabs under the Defense Production Act.

An Ohio manufacturer of cotton swabs has also agreed to convert its facilities to allow for 10 million testing swabs per month.

Testing was an issue on Capitol Hill, too, where the administration and Congress were inching towards agreement on an aid package of more than $450bn to boost a small-business loan programme that has run out of money. The deal is expected to add funds for hospitals and COVID-19 testing, as well.

For most people, the coronavirus causes mild or moderate symptoms, such as fever and cough that clear up in two to three weeks. But for some, especially older adults and people with existing health problems, it can cause more severe illness, including pneumonia and death.