The U.S. has "several more weeks" to go before officials should consider lifting stringent coronavirus mitigation measures such as stay-at-home orders, former Food and Drug Administration Commissioner Scott Gottlieb told CNBC on Tuesday.

"This is going to be a long fight," he said on CNBC's "Squawk Box." "I think we need to keep this going for several more weeks, but there is an end to this, and we know where it is."

States and cities across the country have issued orders closing nonessential businesses and ordering residents to remain mostly at home to curb the spread of the virus. Such measures are devastating to the economy, but Gottlieb, a physician, said they effectively contain the virus in communities where it is spreading largely unchecked.

Standing beside President Donald Trump, members of the White House coronavirus task force said Monday they are assessing when and how to "reopen the country" as the virus spreads rapidly in some regions. Gottlieb, a CNBC contributor who sits on the boards of Pfizer and biotech company Illumina, said new cases in areas hit hard by the virus now likely won't peak for weeks.

"It's going to be another three, four weeks until we see the peak in the epidemic curve in regions like New York, and that's the hopeful case," he said. "Once you hit a peak in the number of cases and you start to come down the epidemic curve you can start to substitute in case-based interventions."

Gottlieb said case-based interventions are more targeted than the population-wide interventions such as school closures and lockdowns. California, New York, Washington State and Illinois have put in place broad restrictions shuttering nonessential businesses and activities. Once community transmission is contained, officials should look to transitioning to more targeted measures, he said.

"You can slowly take your foot off the brake of population-based mitigation and press down on those case-based interventions, and hopefully we'll have more screening in place and that's going to help us do that," he said.

However, in some parts of the country the virus is just picking up speed. New York Gov. Andrew Cuomo said Tuesday that the number of cases in the state is doubling every three days. The virus has now infected more than 49,700 people in the U.S., according to Johns Hopkins University, and killed at least 600 people. Gottlieb cautioned against ending mitigation measures in place before the spread has peaked.

"It doesn't work so long as you have sustained community transmission," Gottlieb said. "We have to break the chain of transmission in areas where this virus is spreading rapidly."

Disclosure: Scott Gottlieb is a CNBC contributor and is a member of the boards of Pfizer and biotech company Illumina.