He gave the warning in a webcast hosted by the National Academy of Sciences.
President Donald Trump is keen on reopening the economy on May 1 with some restrictions.
Trump had declared that a prolonged shutdown combined with “a forced economic depression” could deeply hurt the United States.
The first phase of his reopening process includes the avoidance of groups of more than 10 people where appropriate social distancing is impossible.
It discourages non-essential travel, and encourages telework (working from home) and closure of common areas in offices.
States are also expected to set up screening and testing centres, in addition to developing contact tracing capabilities.
However, Fauci noted that the U.S. was currently averaging between 1.5 million and 2 million tests per week and needs to do more.
“We probably should get up to twice that as we get into the next several weeks, and I think we will,” Fauci was quoted by The Hill as saying.
“Testing is an important part of what we’re doing, but it is not the only part,” he added.
The immunologist stated that high rates of positive results mean that not enough individuals are getting tested.
He stressed the importance of having “enough tests to respond to the outbreaks that will inevitably occur as you try and ease your way back into the different phase”.
Some states have started reopening portions of their businesses over the weekend.
Since the outbreak of coronavirus, the U.S. has recorded 987,000 cases and over 55,000 deaths.