Adm. Brett Giroir, who is overseeing the Trump administration's coronavirus testing efforts, said on Tuesday that he hopes the U.S. will be testing tens of millions of people a month by the fall.

"So by September, taking every aspect of development, authorization, manufacturing and supply chain into consideration, we project that our nation will be capable of performing at least 40 [million] to 50 million tests per month if needed at that time," Giroir said during a virtual hearing before a Senate panel. 

That number would represent a massive increase in the nation's current testing capacity, much of which is handled by the states with some federal support. 

As a whole, the U.S. conducted approximately 1.9 million coronavirus tests last week and has conducted approximately 9 million tests since January. The administration has said it aims to conduct about 12 million tests this month. 

Public health experts have said the U.S. needs to conduct about 5 million tests a week for states to consider safely reopening. The current weekly rate of testing is well below that level, even though several states have begun easing physical distancing measures.