Professor Stephen Powis told LBC, the phone-in and talk radio station, that testing is being expanded and there would be more widespread testing of NHS workers in the next few days.
"We want to get hundreds of thousands of tests ramped up in the next few weeks per day," he said.
The Government is coming under intense pressure to increase testing, particularly for frontline NHS staff so those who are negative can get back to work.
Asked to clarify whether he really meant hundreds of thousands of tests per day, Prof Powis said: "That's what we are aiming for. That is what we want to ramp up to, but remember this is a new virus and we're starting from scratch.
"The kits which are required to do this testing are being manufactured as we speak. We are getting those into the country, we are ramping it up.
"I am talking of hundreds of thousands of tests.
"All of this is ramping up and increasing as we speak but, yes, you heard me correctly, we need to get to hundreds of thousands of tests a day, and we will do that over the course of the next few weeks and we will be making tests available to NHS staff within the next few days."
Figures on Tuesday from the Department of Health and Social Care said Public Health England (PHE) and the NHS are expecting to be carrying out up to 25,000 tests per day within the next four weeks.
Capacity will then continue to be ramped up towards 250,000 tests per day, according to the department.
PHE is working with pharmaceutical giant Roche to increase testing capacity and is also developing a blood test that looks for antibodies against Covid-19.
Such a test will detect those who have already had the virus, allow more accurate estimates of how many people in the population are affected, and the current rate of spread.
Health Secretary Matt Hancock announced earlier this week that a testing facility had opened in Milton Keynes.
He also said the Government had bought 3.5 million antibody testing kits to show whether people have had coronavirus.