Washington (CNN) The US has reached out to South Korea and other nations for help in getting enough supplies to fight the coronavirus pandemic in a sharp counterpoint to President Donald Trump's narrative that the domestic response is enough to combat the crisis.

Seoul's Blue House issued a statement describing a Tuesday call between Trump and President Moon Jae-In that focused on the outbreak. Trump used the conversation to ask Moon if South Korea could provide medical equipment to the United States, the Blue House said. A White House readout of the same call made no mention of Trump's appeal.

The White House request to South Korea appears to be just one of several it has made to allies and other countries for equipment to fight the novel coronavirus . Foreign Policy magazine reported that the State Department sent US ambassadors in eastern Europe and Eurasia to ask their hosts to "ramp up exports and production of life-saving medical equipment and protective gear for the United States."

A senior State Department official said Tuesday that they've "reached out to missions and have asked missions to determine whether certain countries may have excess capacity, the ability to manufacture supplies" and are tracking them with the hopes of matching up "external suppliers, external sources, with states and entities in the US that actually need them."

Trump, meanwhile, has insisted that the US production of equipment needed to meet the viral threat is proceeding apace. But conflicting signals from the administration, the Blue House statement and the increasingly vocal desperation of state leaders were among multiple signals Tuesday that the President's narrative doesn't completely reflect reality.

The White House has not responded to CNN's requests for comment about the Blue House statement. The senior State Department official said they were "not aware of any specific asks of any particular country."

'A tremendous amount'

"The fact is that we are doing a tremendous amount," Trump said Saturday, during a White House coronavirus briefing with reporters. "We started with very few masks. We had some, but nothing for an event like this. And now we're making tens of millions of masks and other things."

On Sunday, Trump again emphasized US readiness. "But we have millions of masks being done. We have respirators. We have ventilators. We have a lot of things happening right now."

But on Tuesday, Defense Secretary Mark Esper said the US military would likely face shortages of medical supplies until the private sector can ramp up production. Federal Emergency Management Agency Administrator Pete Gaynor told CNN on Tuesday that the administration will start wielding emergency federal powers to produce testing kits -- just minutes after Trump insisted those authorities are not needed.

Also on Tuesday, New York Governor Andrew Cuomo gave voice to the frustrations of governors across the country when he blasted the White House response after Trump boasted of sending New York -- now the epicenter of the US outbreak -- 400 ventilators.

"FEMA says, 'We're sending 400 ventilators.' Really? What am I going to do with 400 ventilators when I need 30,000," Cuomo, a Democrat, said at his daily press conference, in which he updated the state's tally to 210 coronavirus-related deaths and 25,665 known infections.

"You pick the 26,000 who are going to die because you only sent 400 ventilators," he said. "I don't need ventilators in six months. And I sure don't need ventilators in five months, four months or three months. ... It is now."

State leaders across the country have been scrambling to make up major gaps in critical medical equipment they need to combat coronavirus as the outbreak spreads rapidly across the country, saying the federal government still isn't fully addressing their pleas for millions of masks, ventilators and other supplies.

As of Tuesday at noon, the US had at least 48,000 coronavirus cases and 600 deaths.

States are feeling enough strain that Republican Georgia Rep. Doug Collins urged Secretary of State Mike Pompeo Tuesday to temporarily ban exports of medical supplies related to the virus, saying that he has heard from state health officials that they are having trouble obtaining equipment because US companies are receiving an influx of European orders.

Cuomo touched on the debate raging between states and the White House and within the administration itself about the Defense Production Act, the 1950 law that allows the federal government to direct domestic production in response to emergencies.

States have said they need Trump to take over distribution because the current process forces the 50 states to compete with one another, the federal government and hospitals to obtain medical supplies.

"Nobody is going to build 40,000 ventilators unless they know someone is going to buy them," Cuomo said, referring to the law's de facto guarantees to companies that the government will buy their production. "That's what the DPA is for. The federal government can say they will buy it."

'Actually going to use the DPA'

While the President is willing to ask other governments for help, so far he has been reluctant to use all the tools at his government's disposal.

Trump has signed the DPA but has not actually used it, bowing to pressure from business leaders who say there are too many unknowns and have instead volunteered to produce whatever is needed to avoid having Trump use those powers. The President reflected their views in a Sunday tweet, saying that when the DPA was announced "it sent tremors" through the business community.

On Tuesday morning, the President took to Twitter again to say, "The Defense Production Act is in full force, but haven't had to use it because no one has said NO! Millions of masks coming as back up to States."

Minutes later, Gaynor told CNN the administration will start wielding "the allocation portion of the DPA" for 60,000 tests kits starting today. While the priorities provision of the DPA is commonly used in emergencies to ensure that government orders get filled first, the allocation portion hasn't been used since the Cold War.

Invoking that element of the law gives the government authority to completely control the entire supply chain, from forcing companies to manufacture critically needed items, to taking over distribution and allocation of those supplies.

"Just a little while ago my team came in and we're actually going to use the DPA for first time today," Gaynor said, speaking with CNN's John Berman.

In addition, FEMA will "insert some language into these mask contracts we have of 500 million masks," Gaynor said. "DPA language will be in that today."

Gaynor's comments caught top White House officials off guard. One said they did not know what Gaynor was referencing and was still trying to figure it out in the hours after he was on television.

Elsewhere in the administration, Esper told a service members' town hall that the US military would likely face some shortages of medical supplies like personal protective equipment, or PPE, until the private sector can ramp up production.

"We have strategic stockpiled medical supplies, we have enough that we were able to offer to the interagency team a supply of masks and gowns and ventilators and things like that," Esper said. "Now, like everybody else, we're going to face shortages with regard to some of the PPE until the private sector industry can pick up the slack."

Esper signaled a shift the Pentagon made Tuesday to limit elective surgeries to free up doctors, nurses and other medical professionals and at the same time reduce the demand for personal protective equipment.

The Pentagon has expressed its thanks to South Korea for supplying coronavirus tests for US military use until American testing equipment arrived on the peninsula. On Tuesday, the Blue House said that South Korea was once again happy to come to Washington's aid.

According to the Blue House, Moon responded to Trump's request for equipment by saying, "If there's spare in the country, (we) will support as much as possible," and telling Trump that FDA approval might be needed for the medical equipment. According to the statement, Trump said he would take action so any South Korean exports could be approved immediately.

The Blue House version of the call contrasts with a White House readout, which said the two leaders discussed "their nations' respective efforts to combat the coronavirus pandemic," but made no mention of the US request for support.

As the US asks its allies for help, China is extending them a helping hand, exporting medical supplies and doctors to pandemic stricken countries such as Italy, where Milan received 25 tons of medical equipment from China Tuesday.