Grant Shapps has denied claims that staff at Covid-hit DVLA offices in Swansea have been told to turn off their NHS Test and Trace apps.
The Transport Secretary told MPs he takes the severe outbreak of coronavirus at the UK Government's Driver and Vehicle Licensing Agency "extremely seriously", but that "no request" for workers to turn off their tracing apps has been made.
It comes as ministers were urged to intervene after 500 cases at the Welsh offices left staff scared to work.
On Wednesday, the DVLA confirmed the death of a member of its staff with the PCS union stating it was "deeply concerned" by the outbreak.
The PCS Union then issued a statement on Thursday threatening to take action if staffing levels at the offices were not reduced.
PCS general secretary Mark Serwotka said: "I have a clear message for DVLA and ministers today - send DVLA staff home or PCS will take the action necessary to keep our members safe.
"It is truly appalling that despite a huge Covid outbreak, over 2,000 people are being forced to work in offices when there was only a few hundred attending the workplace during the first lockdown.
"There is a callous disregard for the safety of our members and a failure to recognise that staff are scared and angry.
"We are deeply concerned and saddened following the news of a staff member dying at DVLA.
"There must be a full investigation into the circumstances."
Earlier during PMQs on Wednesday, the Prime Minister told MPs 2,000 tests had been carried out in the past fortnight, with all results negative, and that Government officials are working "flat out" to deal with concerns.
Raising the issue at transport departmental questions on Thursday, shadow transport secretary Jim McMahon called for allegations that DVLA staff have been told to turn off their phone tracing apps and given warnings for taking time off sick to be "fully investigated".
Mr McMahon told the Commons: "As we all know there have been 500 Covid cases recorded at the DVLA offices in Swansea.
"There have also been worrying allegations that employees have been coerced into turning off their track and trace apps, they were given warnings for taking time off sick and of course these must be fully investigated.
"The evidence offered by the chief executive of the DVLA to the Transport Select Committee has I'm afraid turned a crisis into now a political test.
"Can the Transport Secretary explain why he ignored warnings about this and why he allowed essentially a Government office to become a Covid-19 super spreader?
"And can he confirm if the chief executive of the DVLA still enjoys his full support?"
The Transport Secretary replied: "With regard to DVLA, of course I share (Mr McMahon's) concern about the stories we saw in the newspapers this weekend.
"I have investigated fully.
"I can tell him that only one third of the staff are currently working at DVLA - and he might say why are any of the staff working there - the simple answer is there are paper based and submissions which are not being made online, without which, key workers and others would not be getting their licences.
"There are databases which cannot for privacy reasons be connected to from home which requires some people to go to the offices.
"But a number of very important steps have been taken including working with Public Health Wales, setting up a new office to work in as well.
"And I can tell (Mr McMahon) that no request to turn off Test and Trace, either from DVLA or from DfT have been made.
"And DVLA work under the strict civil service guidance around sick pay and leave and must not diverge from that."
Later, Labour's Paula Barker (Liverpool, Wavertree) told MPs she had heard reports that the "essential work" being carried out at the Swansea DVLA offices including processing personalised number plates.
Ms Barker said: "The Transport Select Committee was told yesterday by the DVLA chief executive that work is being slowed down and that she holds regular meetings with ministers to discuss work priorities.
"Does the minister really believe that activities such as processing provisional licences and even personalised number plates, which I'm told are still being carried out, are priorities for the DVLA during this lockdown?"
Mr Shapps replied: "It is absolutely right that only essential work should be taking place at DVLA and I will check the reports that she mentions."