Officials say 4m tests will be made available each week but decline to estimate how many Americans have been tested thus far

Warning that the number of coronavirus cases in the United States was expected to grow, the Trump administration on Monday said that testing for the virus would ramp up quickly in the coming weeks while declining to estimate how many Americans had already been tested for the virus.

The evening news conference at the White House came as the stock market plunged and an increasing number of Americans wondered how the official count of virus cases in the country, still in the mid-three-figures, could remain so low despite the aggressive spread of coronavirus elsewhere.

Trump addressed economic concerns, telling reporters his administration would ask Congress to pass payroll tax relief and other quick measures. He also said he was seeking help for hourly-wage workers to ensure they’re “not going to miss a paycheck” and “don’t get penalized for something that’s not their fault”.

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“There will be more cases,” the vice-president, Mike Pence, said. “But we simply ask today for the American people to engage in the commonsense practices.”

Donald Trump appeared briefly at the start of the news conference to announce that the administration was considering a relief package for American workers harmed by the outbreak. Trump did not repeat claims he has made on Twitter that political opponents were exaggerating the health risks posed by the virus to antagonize him.

“This blindsided the world, and I think we’ve handled it very, very well, they’ve done a great job,” Trump said.

More than 500 cases of coronavirus have been diagnosed in 35 states and the District of Columbia, not counting cases stemming from repatriation or contained on a cruise ship that docked in California, Trump administration officials said. But the number of actual cases could be much higher, owing to a lag in testing in the US.

Trump convened the news conference as Americans expressed fears that disorganization in federal agencies and mixed messages from the White House about the dangers posed by the virus were delaying an effective response.

The US health secretary, Alex Azar, said he could not estimate how many Americans had been tested for the virus because different tests had originated from and been released to both private and public agencies.

“I could not give you a number of how many Americans have received a test because many have received a test through hospitals or public health labs,” Azar said. He said that the Centers for Disease Control and Prevention (CDC) and two private contractors had so far shipped 1m tests to state laboratories, and he said that by end of week 4m tests per week would be made available.

“We’ve been moving progressively to bring that test closer and closer and closer to the patient,” Azar said.

Leaving the news conference, Trump did not reply to shouted questions about whether he had been tested. At least two members of Congress with whom Trump has recently been in close contact have announced a self-quarantine because they were in contact with a known carrier of the virus.

Pence said he did not know whether Trump had been tested. “I just simply don’t know what the White House physician has recommended to the president,” Pence said. “We’ll let you know tonight.”

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The public was encouraged to visit coronavirus.gov for information about how to combat the virus. “The risk of contracting the coronavirus to the American public remains low, and the risk of serious disease to the American public also remains low,” Pence said.

The surgeon general, Jerome Adams, advised the public to wash their hands, cover coughs and keep a distance from people who are sick. People over the age of 60 are most at risk from the virus, he said, and they are “much more likely to develop complications”. The average age of death from the virus is 80, he said, while children and young adults are “more likely to die from the flu”.

“There is something about being young that is protective,” he said.

Pence urged a protective focus on seniors.

“We’re asking every American to look after our seniors who have underlying health issues,” he said. “They are clearly the most vulnerable.”

The CDC director advised seniors and those with underlying conditions against going on cruise ships. “If you have underlying conditions,” he said, “I would recommend strongly that they do not go on a cruise ship.”

The treasury secretary, Steve Mnuchin, also on hand, blamed the market slide on oil prices and said the “United States has the most resilient economy in the world”.

Pence praised Trump’s leadership in the early stages of the outbreak and said “the vast majority of people who contract the coronavirus will get better”.

“Together we’ll get through the coronavirus,” he said.

Agencies contributed reporting