Matt Hancock has denied he set a target of 25,000 tests a day by mid-April, despite the target being set in a press release by his own department.
Downing Street today revealed that testing capacity now stands at 19,000 people a day, but only 14,982 tests were carried out in the 24 hours up to 9am on Tuesday.
The current capacity falls short of the Government's target to reach 25,000 tests a day by Wednesday April 15.
During today's Downing Street press conference the Health Secretary denied he had set the target, insisting it was set for the end of the month.
But his own department published a press release on its website saying on 18 March. It said: "The increased capacity is expected to be ready within 4 weeks, with highest-priority cases being tested first."
It followed an announcement by Mr Hancock in Downing Street on 17 March.
He told the Downing Street press conferencing there is "spare capacity in the thousands" which gives them the space to increase the number of people eligible.
Some 4,100 social care staff have already been referred for tests, he said.
He said: "We committed to 10,000 tests by the end of March, which we hit, then we had previously committed to 25,000 by the end of April - I increased that goal to 100,000.
"We have hit each of the goals that we have set on testing and we have had the capacity continuing to ramp up this month, the demand has been lower over the Easter weekend as staff haven't wanted to come forward for testing, which is understandable during a long weekend.
"But the goal is still to reach 100,000 by the end of this month."
Meanwhile the Government has insisted it is on track to provide all symptomatic care home residents and social care staff with coronavirus testing - despite appearing to miss its own deadline for expansion.
Health Secretary Matt Hancock said testing is available "right across the NHS and social care for all those who need it" as part of the Government's coronavirus battle plan.
Previous guidance said only the first five symptomatic residents in a care home setting needed to be tested to provide confirmation of whether there is an outbreak.
As well as current residents and staff who need it, testing will also be provided to all potential residents before they are discharged from hospital, Mr Hancock said.
Earlier, experts said the Government must set out how it will rapidly ramp up testing, or risk its pledge being seen as a "false promise".
The NHS Confederation, which represents organisations across the healthcare sector, said the country's testing capacity is "far from where it needs to be".
Dr Layla McCay, NHS Confederation director, said: "Things are improving but the country's testing capacity is far from where it needs to be to meet the ambition of 100,000 a day in just over two weeks."
She added: "We need absolute clarity from the Government on how this will be achieved in such a short space of time, otherwise it will be viewed as a false promise."
The announcement of the rollout follows intense criticism of the Government's treatment of the social care sector, with claims it has been forgotten as the disease spread.
Increases in the laboratory capacity have opened up the chance for the Government to expand testing to include all care home residents who develop symptoms, the Department of Health and Social Care said.
Testing is vital in calculating accurate infection and survival rates. All of the examinations will be PCR (polymerase chain reaction) tests, which search for the presence of Covid-19 in a sample.
The Care Quality Commission (CQC), which is coordinating testing for the care sector, aims to have contacted 30,000 care providers by the end of the week. It has already offered 6,000 care facilities the opportunity to test their staff.
Care providers will then identify workers eligible for testing and refer them to their local testing centre.
On Tuesday, figures released by the Office for National Statistics (ONS) showed that Covid-19 was mentioned on 3,475 death certificates in the week to April 3, including hospital, care home and community deaths.
But care home providers warned they are seeing a higher number of cases and deaths than are officially reported, in part due to a time lag with the ONS figures.
MHA, a charitable operator, said there have now been 210 deaths across 131 of its homes, with outbreaks in about half of its facilities.
Meanwhile, around two thirds of care homes run by Britain's largest care home operator HC-One have seen cases of Covid-19.
