(CNN) The US Centers for Disease Control and Prevention is now counting "probable" cases of coronavirus among its tabulations, according to the agency's website .

The inclusion of such cases will add thousands to the total number of patients and deaths by including people who didn't have a positive test but showed signs of having the virus.

It comes after the Council of State and Territorial Epidemiologists suggested the CDC and state health departments add probable cases.

Previously, the CDC was only counting cases that had been confirmed by them or cases where the agency had yet to confirm a test done by a local or private entity.

A probable case or death is defined as one that meets clinical criteria such as symptoms and evidence of the disease with no lab test confirming Covid-19. It can also be classified as a probable case if there are death or other vital records listing coronavirus as a cause. A third way to classify it is through presumptive laboratory evidence and either clinical criteria or evidence of the disease.

New York City's Health Department said Tuesday it is now reporting "probable" Covid-19 deaths of individuals who have not been tested for the coronavirus but are presumed to be positive. The 4,059 probable cases pushed the death toll in New York City to nearly 11,000 victims.

"The fact is, we have to be honest and always acknowledge the full impact," Mayor Bill de Blasio told CNN's "New Day."

"We think it is smart and really fair to those families and to everyone to say, look, a lot of these deaths ... the medical professionals ... they couldn't confirm it was Covid because there wasn't time do a test but they thought that's what it was."

New York Gov. Andrew Cuomo announced Wednesday that the state will begin counting probable deaths, based on the CDC's guidance.

The CDC count is 605,390 cases of novel coronavirus in the United States and 24,582 people deaths.

According to Johns Hopkins University -- data used by CNN -- at least 637,000 people have contracted the novel coronavirus in the US, and 28,364 people have died.

The US recorded its highest number of coronavirus deaths in a day Tuesday after several days in which the death toll had fallen or was nearly flat.

The daily death toll was 2,405 on Tuesday, according to the Johns Hopkins tally.

Protesters don't want to stay at home

All but seven states are under stay-at-home orders from their governors. And medical experts have said the key to having fewer daily reports of coronavirus is for people to adhere to those edicts.

But in at least two states, groups of people have gone to the state capital to protest, saying their individual freedoms are being trampled on.

In Lansing, Michigan, on Wednesday, several streets around the Capitol were jammed with vehicles in a protest organized by conservative groups against Gov. Gretchen Whitmer, a Democrat.

CNN affiliate WLNS reported that many protesters gathered on the Capitol property.

"It's time for our state to be opened up. We're tired of not being able to buy the things that we need," Brenda Essman of Kalamazoo told the station. "We need to open our businesses."

Another woman told WLNS that her husband was on unemployment for the first time ever.

"We want to go back to work. We have employees. We have bills to pay," Renee Aldrich said. "The only stores open are Walmart. That's ridiculous."

The governor said she understood people were frustrated and respected their opinions. She said she was disappointed in protesters who endangered people by congregating and not wearing masks.

She told reporters she was working on a data-driven approach to reopening.

"I want to be very clear that our decision to reengage sectors is going to be based on the best facts and the best science," she said.

She said if the state acts too early there will be a second wave of cases.

In Raleigh, North Carolina, dozens of demonstrators gathered Tuesday outside the state legislative building to protest the state's stay-at-home order, CNN affiliate WRAL reported.

After an hour, police officers asked the group to disperse, saying too many people were there, too close together. Most left; one person was taken away in handcuffs after refusing to leave, WRAL reported.

Are cases topping out?

Despite the grim numbers, health officials have said they believe US numbers are leveling,

"There's no doubt what we've seen over the last several days is a flattening out," Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said Wednesday on NBC's "Today."

Still, officials are warning that states shouldn't yet ease up on social distancing measures because a resurgence of the virus is highly likely once Americans begin getting out of the house again.

What will be key to preventing another deadly wave in the country are the tools to track and monitor new cases.

"You want your resources to be able to very efficiently in real-time identify, isolate, and contact trace," Fauci said.

In the meantime, finding the right time to reopen the country is still a work in progress.

The US Centers for Disease Control and Prevention is working to make sure testing, contact tracing and an expanded public health capacity is in place as the country begins talking about opening back up, CDC Director Dr. Robert Redfield said.

"This is going to be fundamental to maintain and contain cases as they occur and then make sure we have the health capacity to deal with this, as we work to regain the confidence of the American public that it's safe to go back to work," Redfield said Wednesday on "CBS This Morning."

A team led by the CDC and the Federal Emergency Management Agency has drafted a strategy to return the country to work that includes guidance for local and state governments on how to reopen safely and in phases, the Washington Post reported.

Meanwhile, governors have begun diving into discussions about the first steps toward reopening their economies, with many of the nation's stay-at-home orders, as well as the federal government's social distancing guidelines, set to expire at the end of the month.

But many state leaders who are still seeing their number of cases climb say it's too soon to begin thinking about lifting any measures.

Some hospitals want to do elective surgeries again

The Yuma Regional Medical Center is losing more than $400,000 a day because of a state pause for elective surgeries and procedures, according to hospital CEO Dr. Robert Trenschel.

He wants the ban, which is designed to help conserve protective equipment and prevent Covid-19 spread, to be lifted.

Likewise, the Washington State Hospital Association has asked for a modification of the order to cancel non-urgent procedures to allow "procedures and surgeries that have the most chance of causing patient harm if they're not done."

Trenschel pointed out the Arizona county the hospital is in has only had about 20 cases of Covid-19. He's spoken with Gov. Doug Ducey, Sen. Kyrsten Sinema and US representatives to encourage them to allow elective procedures at facilities like his, but he said he's gotten nowhere.

His hospital has seen nine coronavirus cases, which hasn't caused a burden on the facility, he said. They still have the capacity and resources to do elective procedures -- and they want to do them.

"We're not allowed to do surgery on patients that want it, surgeons that want to do it. And we can do it safely," Trenschel said.

In Washington, the hospital association wants to focus on patients that "may be in danger of losing their health insurance due to furloughs" or being laid off, said Cassie Sauer, president and CEO of the organization. She added that delaying health care is detrimental to the health of some patients.