The Secaucus, N.J., company, one of the biggest diagnostic-testing providers in the country, last month was averaging a turnaround of seven days as demand outpaced its capacity to process the tests.
A week ago, Quest said the turnaround time was down to two to three days.
The current estimate includes what it calls the priority population, for example, "hospitalized patients, patients and staff in long-term healthcare settings, such as nursing homes, and presurgical patients in acute-care settings."
The company also said it had completed testing and reporting results of all its test specimens outstanding that were associated with a recent surge in tests.
"Turnaround time can fluctuate with demand and vary by region," Quest said in a statement.
Covid-19 "is unpredictable and changing dynamics affecting demand, supplies and other factors could cause turnaround times to slip."
Quest says that its current capacity is 150,000 covid-19 tests a day and it expects to increase that figure to 185,000 by Labor Day. And it may be able to increase capacity further beyond that Sept. 7 target.
Turnaround time for the tests includes the time required to transport specimens to Quest laboratories, the company said.
Access to rapid testing has been touted by health officials and former Microsoft Chairman Bill Gates as one of the keys to overcoming the coronavirus pandemic.
The U.S. has been one of the world's hardest-hit countries, with 5.44 million confirmed coronavirus cases and more than 170,000 deaths.
At last check Quest shares were off 0.6% to $119.28. The stock is up more than 17% year to date.