President Donald Trump on Monday put a string of top private industry executives on the microphone at the Rose Garden at the White House, to pledge dramatically ramped-up testing for Covid-19, seen as critical to a sustainable return to business.

The announcement came as several states cautiously began to allow some suspended activities to resume, even as the United States the very next day surpassed one million infections. The coronavirus has killed more than 59,000 people in the country.

Testing has been the country's Achilles heel, with the first batch of faulty tests causing the US to lose an entire month in terms of surveillance for Covid-19.

The White House announcement was essentially a blueprint for testing, in which implementation will be the responsibility of individual states, with the federal government providing strategic direction and technical assistance.

On Tuesday, New Yorkers were able to get tests done on demand for the first time. In Washington DC, a mobile phone message to residents from Mayor Muriel Bowser outlined how they could get free tests if they have symptoms of the coronavirus.

"That's something that wasn't fully in place early on but right now there's a commitment," said Dr Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases at the National Institutes of Health.

"I believe we are much, much better off now than we were several weeks ago."

Thousands of jobs related to contact tracing are expected to become available in the next few weeks as states beef up their capabilities.

There are two kinds of tests - one which detects the coronavirus in an infected person, and one which detects if a person has been previously infected.

The first test is available in different forms, with some results being rapid and some taking more than a day or two. The second measures the antibodies in the system, which are produced when the body fights the virus.

Dr Mark McClellan, a physician and economist who directs the Duke-Margolis Centre for Health Policy, told journalists last Saturday that the US is probably doing well over a million tests per week, but noted that there are still significant outbreaks around the country and that tests are not being used optimally yet.

"I think you're going to see some progress in that area over the next couple of weeks," added Dr McClellan.

Dr Fauci on Tuesday acknowledged the late start to testing.

"However, we have responded now in a very aggressive way, and appropriately, in the way our country is built. Namely, we have engaged the private sector, the big companies who know what they're doing, who do this for a living," he told The Economic Club, a forum in Washington DC.

"The testing situation has improved very rapidly," he said. "Whether or not we're exactly where we want to be, that remains to be seen. I think we are either there or getting very close to being there."