U.S. health officials see "glimmers" that social distancing efforts to slow the spread of the coronavirus are beginning to dampen the outbreak, White House health advisor Dr. Anthony Fauci said Tuesday.

Americans are still "in a very difficult situation," the director of the National Institute of Allergy and Infectious Diseases said on CNN. "We hope and I believe it will happen that we may start seeing a turnaround, but we haven't seen it yet. We're just pushing on the mitigation."

"You don't want to get overconfident. You just want to keep pushing," he added.

The rate of new hospitalizations from COVID-19 in places such as New York are beginning to slow and are "possibly" beginning "to flatten out," Fauci said.

U.S. cases reached more than 164,000 as of Tuesday morning, with more than 67,000 in New York state, according to data compiled by Johns Hopkins University. U.S. deaths surpassed 3,000, more than the number of people who died in the Sept. 11, 2001, terror attacks. The death toll is expected to rise over the next few weeks as more patients flood hospitals, U.S. officials say.