Anger is mounting in the US over the Trump administration’s failure to test for coronavirus on a scale that could contain the outbreak and mitigate its most devastating impacts.

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On Thursday the lack of testing capacity for Covid-19 was recognised in blunt terms by one of the top US officials dealing with the crisis. Dr Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, described the current state of affairs as “a failing” at a hearing of the House oversight committee.

From Congress to state capitals across the country, politicians of both main parties have shown rare bipartisan agreement that the pace of federal testing is woefully inadequate. Congress members who were given private briefings by Trump administration officials on Thursday expressed shock and outrage that so far only 11,000 tests have been conducted in a country of 327 million people.

By contrast South Korea, which has been grappling with one of the most severe outbreaks of Covid-19 globally, tests roughly the same number, about 10,000 people, every day. In total, South Korea has tested 230,000 of its 51 million people – 130 times as many per capita as the US.

The aggressive use of testing to identify carriers of the disease and quarantine them has been credited as a major factor in South Korea’s relative success in dealing with the crisis.

Answering press questions in the Oval Office on Thursday, Trump said: “Frankly, the testing has been going very smooth.” He added: “We have heavily tested.”

That is factually incorrect, and a growing number of public officials, including from his own party, are willing to say so.

Members of Congress who attended a bipartisan House briefing expressed anger about testing failures.

Mike Quigley, a Democratic congressman from Illinois, said: “We are not where we need to be and not sure when we are going to get there. We are flying blind.”

Mark Walker, a Republican congressman from North Carolina, told CNN that there was “a growing frustration among members as a whole to get more definitive answers”. The Republican senator and former presidential nominee Mitt Romney of Utah said: “Our system has just not been up to snuff and I think a lot of people are frustrated by it. I’m one of them.”

Andrew Cuomo, governor of New York, which is one of the states hardest hit by the disease so far, told CNN the US was “way behind on testing”. What he called a “federal bottleneck” was so bad that he had authorised New York authorities to contract out testing to private laboratories.

Cuomo said the paucity of testing not only prevented containment of localised outbreaks, it also gave the public a false sense of security by obscuring how prevalent the disease has already become. “It’s because we have no testing capacity, that’s why the numbers are low. If you actually had testing capacity you would see how high the numbers are already. As we do ramp up testing you are going to see those numbers go sky-high.”

• This article was amended on 16 March 2020. An earlier version referred to the number of specimens tested for Covid-19 in the US on March 10 by the Centers for Disease Control and Prevention (CDC) and public health labs. The figure at the time was just eight, but this was an incomplete figure. The CDC’s coronavirus database indicates that the final figure for March 10 was 2,587. We have removed the section in question.