Teaching unions warned against opening schools in June, calling the plans “reckless” and “irresponsible”.
In the letter, Chaand Nagpaul CBE said: “The view of the members of the Public Health Medicine Committee is completely aligned with the NEU that, until we have got case numbers much lower, we should not consider reopening schools.
“The NEU is absolutely right to urge caution, to prioritise testing and to protect the vulnerable.We cannot risk a second spike or take actions which would increase the spread of this virus, particularly as we see sustained rates of infection across the UK.”
He told Kevin Courtney that the government would “do well to heed” the union’s advice.
This comes as council leaders said schools should be allowed to make their own decisions about reopening - especially in areas where there is a higher proportion of black, Asian and minority ethnic residents.
The Local Government Association (LGA) is calling for some schools in England, in consultation with councils, to be given greater flexibility locally over reopening as they argue that some communities are at higher risk.
It comes after an analysis by the Office for National Statistics suggested that black men and women are more than four times more likely to die a coronavirus-related death than white people.
The LGA wants councils to be given more powers to close schools if testing indicates clusters of new Covid-19 cases - and it says the Government should urgently publish the scientific evidence underpinning the decision to reopen England's schools to more pupils from June 1.
Coun Judith Blake, Leeds City Council leader and chairwoman of the LGA's Children and Young People Board, said: "We know parents are anxious about sending their children back to school or nursery. Plans to reopen schools and early years settings must focus on reassuring parents that it will be safe for children to return to school.
"Publication of the scientific advice is vital to help provide that reassurance. The safety of staff, parents and families is absolutely paramount."
Mary Bousted, joint general secretary of the National Education Union, said: "We agree with the LGA that publication of the scientific advice is vital to help provide reassurance to the public."
She added: "We have concerns that a wider opening of schools, too early, poses a lot of unanswered questions about the risks in poor communities.
"The DfE has not done nearly enough thinking about the emerging evidence about the racial disparities of the epidemic and what it means for schools with diverse pupil populations."
Appearing on Radio 4's Today programme with Dr Bousted on Thursday, former Labour education secretary Lord Blunkett said he was "surprised" by union leaders' attitude towards reopening schools.
He said: "I am being deeply critical of the attitude. It's about how can we work together to make it work as safely as possible. Anyone who works against that in my view is working against the interests of children."
The Government's Covid-19 recovery strategy said its ambition was for all primary school children to return to school before the summer holidays for a month "if feasible".
But the National Association of Head Teachers, whose members are mainly in primary schools, has advised school leaders not to plan for a full reopening from July at present.
Education Secretary Gavin Williamson said: "When you have medical and scientific advice that is saying it's the right time to start bringing schools back in a phased and controlled manner, it seems only the right thing to do and the only responsible thing to do."
A DfE spokeswoman said: "We want children back in schools as soon as possible because being back with their teachers and friends is so important for their education and their wellbeing.
"Plans for a phased return of some year groups from 1 June, at the earliest, are based on the best scientific and medical advice. The welfare of children and staff has been at the heart of all decision making.
"We have engaged closely with the unions throughout the past seven weeks and will continue to do so, including to develop further guidance for the sector."