Massachusetts has a goal of conducting a minimum of 3,500 coronavirus tests each day, Gov. Charlie Baker said Thursday, and is on track to get to that level through "an enormous increase" in testing capacity by early next week.

Baker, Lt. Gov. Karyn Polito and Health and Human Services Secretary Marylou Sudders toured Quest Diagnostics in Marlborough on Thursday morning as the lab ramps up to be able to test 20,000 people per day across the country. CEO Steve Rusckowski said the company hopes to eventually be able to test 2,000 to 3,000 people a day in Massachusetts.

"We believe that over the course of the next several days and weeks there will be an enormous increase in the amount of testing that takes place on a daily basis here in the commonwealth of Massachusetts," Baker said. "It can't happen fast enough but I do believe that with the pivots and the adjustments that are being made by organizations like Quest here in Marlborough and by many of our hospital p artners and by the state lab and other organizations, we will get to the point where we're doing the amount of testing every day that we believe that we need to be doing."

The Department of Public Health reported Wednesday that the state lab had conducted 1,743 coronavirus tests as of 7:30 a.m. Wednesday. Of those, 224 were identified as positive cases of infection.

As of 11:30 a.m. Wednesday, LabCorp has conducted 306 tests resulting in 11 positive results, Quest Diagnostics has run 222 tests leading to 12 positives and the U.S. Centers for Disease Control has confirmed the other nine positive cases. Sudders said Thursday that, using South Korea as a model, Massachusetts needs to be testing 3,500 people each day at a minimum. Baker said that amount of testing should help the state be able "to play a proactive game here."

"It would be a good place to build from in our state," Sudders said. Massachusetts officials confirmed the state's first positive COVID-19 case on Feb. 1.