Stock marked indices sharply rallied during Trump's press conference , posting their largest single-day gain since October 2008. The Dow Jones Industrial Average closed 1,985 points higher, or 9.4%, at 23,185.62., the index's biggest-ever point gain on a single day.
The emergency declaration will free up as much as $50 billion in financial resources to efforts by states and U.S. territories to assist Americans affected by the outbreak.
But Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, warned, "There will be many more cases" of coronavirus in coming weeks.
As of Friday, the number of positive tests for people in the United States with coronavirus had reached 2,006, according to NBC News. At least 42 people in the country have died after contracting the virus.
Trump announced the national emergency declaration at a news conference in the Rose Garden at the White House, where he was joined by Vice President Mike Pence, who is leading the administration's coronavirus task force.
"To unleash the full power of the federal government ... I am officially declaring a national emergency," Trump said. "Two very big words."
"The next eight weeks are critical," the president said.
If they should be tested, under the website's criteria, they will be directed to "drive-thru" sites, so so that people can stay in their cars when they are screened for the virus, according to officials. Trump said Google has 1,700 engineers working on the effort now.
But Trump and his officials appear to have overstated the current state of the tool, which is being developed by Verily, the life sciences sister company to Google. Both are Alphabet companies.
Google's communications team said in a statement, "We are developing a tool to help triage individuals for Covid-19 testing."
"Verily is in the early stages of development, and planning to roll testing out in the Bay Area, with the hope of expanding more broadly over time," the statement said.
Trump said he expected the U.S. to have 1.4 million coronavirus test kits available within a week, and a total of 5 million kits within the next month. He then said he doubted the country will "need anywhere near" 5 million kits.
Trump was asked by a reporter if he took responsbility for what Fauci earlier in the week called "a failing," in reference to the lag so far in testing Americans.
The president replied, "No, I don't take responsibility at all."
"Because we were given a ... set of circumstances, and we were given rules, regulations and specifications from a different time," Trump said. "It wasn't meant for this kind of an event with the kind of numbers that we're talking about."
Trump said he had ordered all states to set up emergency operation centers, and urged hospitals to engage emergency operation plans.
But, Trump said, "we don't want people to take a test if we feel that they shouldn't be doing it, and we don't want everyone running out and taking. Only if you have certain symptoms."
Trump said he "most likely" will himself undergo testing for coronavirus, but noted that he does not have any symptoms.
Trump last week posed for a photo at his Mar-a-Lago resort in Florida with the press secretary for Brazil's president, Jair Bolsonaro, who has tested positive for the virus.
Bolsonaro, who had dined with Trump during that visit, tested negative for coronavirus, his son announced Friday.
Trump said the emergency declaration will grant new authority to Health and Human Service Secretary Alex Azar to waive rules governing how hospitals take in patients, and how long they can stay.
Seema Verma, the administrator of the federal, Centers for Medicare and Medicaid Services, announced that all visitations to nursing homes would be suspended except in certain cases, such as a resident dying.
Trump also announced that he was waiving all interest on student loan debt held by the federal government.
Trump dismissed as "a nasty question" a query from a reporter about how he can claim he is not responsible for a lag in testing people for coronavirus when his administration in 2018 dissolved a National Security Council group that was tasked with preparing for pandemics.
"I didn't do it," Trump said of the group being disbanded.
"You say we did that. I don't know anything about it."
But Fauci only two days ago had publicly commented on negative impact from the dissolution of the group.
"We worked very well with that office. It would be nice if it were still there," Fauci said at a House Oversight and Reform Committee hearing
In 2018, Trump fired Tom Bossert as the NSC's homeland security adviser, whose responsibilities included coordinating the response to global pandemics. Bossert was not replaced.
As Trump ended the press conference, which lasted more than an hour, he walked away without answering as a reporter asked if he could explain why his recent prediction that the number of coronavirus cases would soon go down to close to zero had not come true.
The Senate's top Democrat, Sen. Chuck Schumer of New York, said, "I'm pleased the president heeded our calls to invoke the Stafford Act to extend vital financial assistance to help keep communities safe from the coronavirus outbreak."
"I urge New York and other states to immediately request these newly available funds and for the Trump administration to approve these requests without delay," Schumer said.
"As other steps are considered, the president must not overstep his authority or indulge his autocratic tendencies for purposes not truly related to this public health crisis."
Trump's emergency designation under the Stafford Act allows for two types of presidential declarations.
The first is an emergency, which Trump declared.
The second is a major disaster, which gives emergency management even more access to resources.
Both designations place FEMA in charge of what happens.
French President Emmanuel Macron said earlier Friday that he, Trump and the rest of leaders of the Group of 7 economic giant nations have "agreed to organize an extraordinary Leaders Summit by videoconference on Monday on Covid-19."
"We will coordinate research efforts on a vaccine and treatments, and work on an economic and financial response," Macron announced in a tweet.
The announcement of a U.S. national emergency came just a day after Trump said he was not yet ready to make such a declaration.
"We have very strong emergency powers under the Stafford Act, and we are — we have it — I mean, I have it memorized, practically, as to the powers in that act. If I need to do something, I'll do it," Trump had said in an Oval Office meeting on Thursday with Ireland's prime minister, Leo Varadkar.
"I have the right to do a lot of things that people don't even know about," Trump said.
An emergency declaration puts to rest weeks of debate within the White House, where different factions of Trump's top aides disagreed about whether a Stafford Act declaration is necessary.
Those opposed to making the declaration, which had included Trump himself, worried that it would cause financial markets to panic.
They also feared political fallout if it appeared Trump was sending the opposite message about coronavirus, namely that it is an emergency, from the one he had consistently delivered so far.
Trump has claimed that coronavirus is no more dangerous than the common flu, and that it will likely disappear quickly and without a significant impact on American life. Health officials say neither of these statements is accurate.
New York Mayor Bill de Blasio declared a state of emergency in the city on Thursday. New York Gov. Andrew Cuomo on the same day banned gatherings of 500 or more in the state "for the forseeable future."
Treasury Secretary Steven Mnuchin told CNBC earlier Friday the White House and Congress are nearing a deal that would provide stimulus to the U.S. economy amid the coronavirus outbreak.
"I think we're very close to getting this done," Mnuchin said in a "Squawk on the Street" interview.
"The president is absolutely committed that this will be an entire government effort, that we will be working with the House and Senate."
But during the press conference, Trump said he problems with the plan announced Friday afternoon by House Speaker Nancy Pelosi, D-Calif.
There was no deal between Congress and the White House as of early Friday evening.
As of Friday, there were more than 135,000 known cases of coronavirus globally, including nearly 5,000 deaths, according to data compiled by Johns Hopkins University.
In the United States, there have been at least 1,700 known cases, with at least 40 deaths, according to Johns Hopkins University.
Correction: An earlier version misstated when the mayor declared an emergency in New York City. It was Thursday.
— Additional reporting by CNBC's Yelena Dhzanova