The first human trial of a vaccine to prevent the coronavirus could advance to the next step this spring, Moderna Chairman Noubar Afeyan said Thursday.

"It's difficult to put a specific date on things just because it's a very dynamic situation," Afeyan told CNBC's Meg Tirrell. "We've entered phase 1 trials. ... We'll enter hopefully phase 2 trials, we expect that to happen in the spring, perhaps early summer."

"And success there will hopefully lead us to phase 3 trials," Afeyan added on "The Exchange."

Moderna partnered with the National Institutes of Health to accelerate the development of the vaccine to prevent COVID-19. Phase 1 human trials of the potential vaccine began in the Seattle area in mid-March.

The trial was launched in "record speed," Dr. Anthony Fauci said at the time. Fauci, a White House health advisor and the director of the National Institute of Allergy and Infectious Diseases, said Wednesday that the trial was "on track" and public distribution was still projected in 12 to 18 months.

The development of a vaccine to prevent COVID-19 continues to grow in importance as more than 981,000 people worldwide have been infected by the disease. More than 50,000 people have died, according to Johns Hopkins University data.

Afeyan, who is also CEO of venture capital firm Flagship Pioneering, helped co-found Cambridge, Massachusetts-based Moderna in 2010.

Afeyan said he expects other companies working on a vaccine, such as Johnson & Johnson, could also be successful in developing an effective one.

"We hope that everybody succeeds because the worldwide demand for these types of interventions is far in excess of what any one player can deliver," he said.

Johnson & Johnson said Monday that it hoped to begin human trials of its experimental COVID-19 vaccine by September.

Other companies are attempting to develop a drug to treat COVID-19.

Former Food and Drug Administration Commissioner Scott Gottlieb told CNBC on Thursday that he hoped to see the same urgency around a vaccine be applied to a COVID-19 drug.

A vaccine is the long-term solution, but an effective drug could be developed more quickly, contended Gottlieb, a CNBC contributor who sits on the boards of Pfizer and biotech company Illumina.

"This virus isn't going away. It's going to continue to bounce around the world," Gottlieb said. "And it's going to change our lives until we have a therapeutic that can vanquish it or really take the fear away from this virus spreading in the background."