Gottlieb told CBS News' Face the Nation that the United States should stand by its plan to deliver doses to states based on population side as he expects supply to exceed demand in as early as three weeks.
"I think a lot of states are going to see themselves with excess supply and excess appointments. So it's going to be a shame and look back in retrospect and realize that we probably should have put more vaccine into some of these hot spots to snuff them out earlier," he said.
The United States has reported a total of 31,189,567 COVID-19 cases and 562,059 deaths since the start of the pandemic as of Sunday -- both the highest totals in the world -- while reporting 66,533 infections and 709 fatalities from Saturday, according to data gathered by Johns Hopkins University. The nation has also administered a total of 183,467,709 vaccine doses with 35.3% of the population having received at least one dose and 21.3% fully vaccinated, according to the Centers for Disease Control and Prevention.
Gottlieb's comments came amid a surge of virus cases in Michigan as the state, which does not report COVID-19 data on Sunday, tallied 6,892 new cases and 74 deaths on Saturday, after reporting 7,834 cases Friday for a total of 738,023 cases and 16,500 cases since the start of the pandemic.
Michigan Gov. Gretchen Whitmer on Sunday told Face the Nation has asked the White House to provide the state with additional vaccines to combat the surge and asked the state to take a two-week "pause" including urging high schools to suspend in-person classes, youth sport games, and indoor dining and gatherings.
"Right now, we know we've got even greater capacity. We could get more vaccines in arms. And when there's a surge, we think it's important that we rush in to meet where that need is, because what's happening in Michigan today could be what's happening in other states tomorrow," Whitmer said.
Gottlieb said the White House should adopt a habit of surging COVID-19 resources to hotspots.
"They never perceived that there was going to be a confluent national epidemic, but there were going to be localized outbreaks," he said. "That, in fact, is likely what we're going to see going forward. We're not going to see a confluent epidemic, but we'll see those hotspots, so we need to get in the habit of trying to surge resources into those hotspots to put out those fires of spread."
Elsewhere, Los Angeles opened vaccination appointments up to residents 16 and older as the state prepares to expand vaccine eligibility to those in that group.
California reported 4,954 new cases and 105 deaths on Sunday, noting that the tally includes cases from previous months that had not been counted. Since the start of the pandemic, California leads the nation with 3,600,178 cases and 59,218 deaths.
To date, California has administered 22,777,893 vaccine doses with 6,294,860 people fully vaccinated.
Texas ranks second in cases with 2,422,139 since the start of the pandemic along with 48,211 deaths after reporting 1,516 new cases and 26 fatalities on Sunday. The state has administered 14,312,547 vaccine doses with 5,613,265 people fully vaccinated.
Third-ranked Florida reported 5,520 new infections and seven resident fatalities on Sunday, bringing its totals to 2,124,233 cases and 34,021 resident deaths. Florida has administered 11,161,697 vaccine doses with 4,400,166 people fully vaccinated.
New York ranks fourth in the nation with 1,949,964 cases and second in 51,036 deaths since the start of the pandemic as it added 6,764 new positive tests and 53 deaths Sunday. New York has administered 11,811,282 vaccine doses and 4,871,118 people have been fully vaccinated.
Illinois has the nation's fifth-greatest total of COVID-19 cases at 1,279,772 along with 21,505 fatalities adding 2,942 infections and 16 deaths on Sunday. A total of 7,047,326 COVID-19 vaccines have been administered in the state and 2,853,739 people have been fully vaccinated.