Justice Secretary Robert Buckland was challenged on BBC Breakfast about trust in the government after his ministerial colleague Therese Coffey wrongly claimed that more than 100,000 people had been tested for coronavirus on some days.
Presenter Louise Minchin said that in fact there was "not a single day" when more than 100,000 people had received tests, and asked him if claims like these undermined trust.
Mr Buckland said the government needed to be "straightforward", adding that where there had been difficulties "everybody has known about it".
He also acknowledged that the planned contact tracing system and app were "still very much work in progress" and might not be "full-blown" by the time schools are due to open on 1 June.
Mr Buckland said the government needed to "listen very carefully" to schools concerned about readmitting more children and acknowledged that there may not be a "uniform" return to teaching.