The U.S. is not even "remotely prepared" to re-open, an expert said on Tuesday as some states are set to lift lockdowns that had been imposed to contain the coronavirus outbreak.

"We're not remotely prepared neither in terms of the epidemiology of the outbreak in the United States, nor in terms of our preparedness capacities to begin suppressing this virus in ways other than through social distancing," said Jeremy Konyndyk, senior policy fellow at the Center for Global Development, a think tank. His expertise includes global outbreak preparedness.

The U.S. has reported more than 988,000 confirmed cases of infection and a death toll of over 56,000 so far, according to John Hopkins University.

The pandemic, which first emerged late last year in the central Chinese city of Wuhan, has prompted U.S. states to impose strict social distancing policies in order to contain the outbreak. These measures, including closing nonessential businesses and ordering residents to stay home, have led to a devastating economic rout.

But states including Alaska, Georgia, South Carolina, Tennessee and Texas are beginning to allow restaurants and other establishments to serve customers. Ohio Gov. Mike DeWine said consumer retail and services can start reopening on May 12.

New York Gov. Andrew Cuomo said Sunday the state plans to reopen its economy in phases.

However, the ongoing lack of testing capabilities is one of the main factors keeping many families, employers and institutions from resuming business, even though stay-at-home orders have officially been lifted in several states.

While some states have been more aggressive in testing, Konyndyk told CNBC's "Squawk Box Asia" that the country at large is not seeing a decline in coronavirus infections and that there needs to be more testing.

"We need to be able to test widely, we need to be able to trace the contacts of those cases that we find, we need to reinforce the hospital system and we need to do far more to protect people in high risk facilities like elder care homes. None of that is in place yet," said Konyndyk. "So no, we are not remotely ready."

Testing 2% of people in each state monthly would be a major jump — roughly 1.6% of the U.S. population has been tested in total so far, according to the Covid Tracking Project.

Yet some experts say the country needs to perform closer to 20 million to 30 million tests a day to begin getting the economy back to normal, due to concerns about pre-symptomatic and asymptomatic transmission.

"Right now, we've got much of the country quarantined, so if someone gets sick, the chances they can spread to others are smaller," said Konyndyk.

"If you begin reopening before you have the ability know who's sick, or frankly, before those people have the ability to know they have it, you run into enormous risks," added Konyndyk.

Citing examples from places like Japan's Hokkaido where strict curbs were lifted too soon, Konyndyk raised concerns about subsequent waves of infections.

"We will face second waves and third waves of this even under the best of circumstances. But if we reopen too early, we're going to be be much worse because the virus now is seeded so much more widely throughout the country, there are a lot more people who can potentially spread it."

Rushing to reopen could "torpedo" both economies and public health, he said.

"It's not like you can pick one or the other. You have to get the health back on track in order to get the economy back on track," said Konyndyk.

CNBC's Christina Wilkie and Kevin Breuninger contributed to this report.