The United States could see “staggering” numbers of coronavirus deaths in the coming months as infection rates increase during the colder months, Dr. Scott Gottlieb told CNBC’s “Closing Bell” on Friday.There were 1,038 deaths from Covid-19 in the U.S. on Thursday, the largest total since late September, according to data compiled by the Covid Tracking Project, an independent volunteer organization launched by journalists at The Atlantic. New coronavirus cases eclipsed 71,600 on Thursday.Gottlieb, a physician who served as the U.S. Food and Drug Administration commissioner, emphasized that doctors have improved their treatment of Covid-19 patients during the pandemic, bringing down the mortality rate. He has said it might have been reduced by 50%.Patient care also has been improved due to drugs such as Gilead Sciences’ remdesivir, which on Thursday became an FDA-approved treatment for Covid-19, as well as the use of steroids such as dexamethasone, according to Gottlieb. President Donald Trump received both after his coronavirus diagnosis.Despite these positive developments, Gottlieb said the challenge the U.S. is facing now is simply how widespread the virus is across the country. “Mortality is going to be down, but we’re going to be infecting so many people that the daily death statistics are going to be staggering,” said Gottlieb, who led the FDA under Trump from May 2017 to April 2019.There could be “well above 1,000” new deaths per day reported in the weeks ahead, he said. “And we might retest some of the totals that we saw in the spring, when we were reporting 2,000 deaths a day related to this virus, just because of the sheer number of people we’re likely to infect heading into the winter right now.”The U.S. has almost 8.5 million confirmed cases of Covid-19 and at least 223,752 people have died, according to data compiled by Johns Hopkins University.Public health experts have been warning for months that colder weather during the fall and winter is likely to coincide with a resurgence of the coronavirus because people are spending more time indoors, where transmission can more easily occur.The pandemic is intensifying in countries across the world, and some nations are on a “dangerous track,” the head of the World Health Organization warned Friday. “We are at a critical juncture in this pandemic, particularly in the Northern Hemisphere,” Director-General Tedros Adhanom Ghebreyesus said.Restrictions have again been implemented in parts of Europe, including an overnight curfew in regions of France, in an attempt to reduce the spread of Covid-19.Gottlieb said he believes the response in the U.S. to rising infection rates will be targeted interventions in hot-spot areas, rather than the lockdown orders that were issued in the early stages of the pandemic when inadequate testing regimes made it difficult to determine where transmission was happening.”I think we’re going to bear a lot more infection … and the health-care system is going to have to bear the brunt of this burden, because I don’t think you have the popular will for stay-at-home orders or broad mitigation,” he said.”If everyone would just wear masks, that would cut down on the spread,” he added.— CNBC’s Noah Higgins-Dunn contributed to this report.