Sen. Bernie Sanders, I-VT, asked CDC Director Robert Redfield during a hearing on the coronavirus about the new policy, which was announced Friday.
Redfield told members of Congress that the policy is currently under "critical review" at the agency as he said it doesn't send the right message to Americans amid a pandemic.
"Obviously, when they announced that the other day, there was substantial disappointment with American Airlines," he told the Senate Health, Education, Labor and Pensions Committee during a hearing on U.S. efforts to contain the coronavirus pandemic. "We don't think it sends the right message."
American Airlines said Friday that it will continue to notify passengers when their planes are full and allow them to switch to less-crowded flights at no extra cost through Sept. 30. The company said passengers with flights booked through Sept. 30 can also change their flights, including adjusting origin and destination cities, without incurring a travel change fee but will have to pay for any difference in the fare.
The announcement from American Airlines came as Covid-19 cases continue to soar throughout the United States. As of Monday, new cases grew by 5% or more in at least 40 states, based on a seven-day average, including Arizona, Texas, Florida and Oklahoma, according to a CNBC analysis of data compiled by Johns Hopkins University.
Airlines are scrambling to ensure travelers feel safe flying during the pandemic as demand remains low. While much higher than the five-decade lows hit in April, the number of people passing through U.S. airport checkpoints is still less than a quarter of the levels seen during June 2019, according to federal data.
Some airlines including Delta, Southwest, JetBlue and Frontier continue to limit capacity onboard. United, which hasn't been limiting bookings on flights, notifies travelers when their planes are filling up and allows them to change to another. American also does that and will continue to do so.
"We are unwavering in our commitment to the safety and well-being of our customers and team members," American said Tuesday in a statement to CNBC. "We have multiple layers of protection in place for those who fly with us, including required face coverings, enhanced cleaning procedures, and a pre-flight COVID-19 symptom checklist — and we're providing additional flexibility for customers to change their travel plans, as well."
Scientists say the virus can spread through respiratory droplets that pass when an infected person coughs or sneezes. It can also spread on surfaces like airplane seats and tray tables. Scientists and public health officials fear that passengers crammed in an aircraft could be a breeding ground for the virus.
Some industry members have warned that physical distancing on aircraft is extremely challenging.
"You can't employ distancing on an airplane like you can on a grocery store line," said Nick Calio, CEO of Airlines for America, an industry group that represents major U.S. airlines including American and United.
Major U.S. airlines now require passengers to wear masks and also that they answer questions about their health before flying.
Whether it's a bus, train or a plane, social distancing and a face covering are important, Redfield said Tuesday.
— CNBC's Hannah Miller contributed to this report.