The U.S. economy is on a positive trajectory, but it is still in a "deep hole" and a rise in coronavirus infections could slow growth, New York Federal Reserve Bank President John Williams said Friday.

"The very large rise in COVID cases recently clearly puts a question market on the ability of the economy to weather this period," Williams said in an interview with the Financial Times. "I would expect the growth in the fourth quarter, and maybe into early next year to slow somewhat."

The ability to fully move past the virus will depend on the development of vaccines and other therapeutics, and progress announced recently on those fronts offered "positive signs" about the ability to move beyond Covid-19 in the next year or so, Williams said. Pfizer Inc announced earlier this week that its experimental COVID-19 vaccine is more than 90% effective, according to initial trial results.

Despite that good news, Williams said he is still more concerned about inflation remaining too low over the next several years as the economy continues to heal and millions of people try to get back to work.

"Things are looking better, but that's in context of an economy that took an enormous hit," Williams said. "Even today unemployment is still very high and we're still in a deep hole."

The fiscal aid rolled out by Congress earlier this year helped Americans stay afloat, and the savings built up with the help of stimulus checks and unemployment benefits are still supporting the economy today, he said.

"The reason consumers are still able to spend, the reason the economy is still going, is that we know that people are still having some of the unemployment checks and stimulus checks that they got," Williams said. "That's giving them the ability to pay the rent, put food on the table."