The planned reopening of schools in England on 1 June is not feasible, head teachers and council leaders have said.
National Association of Head Teachers head Paul Whiteman told MPs that, as his union understood official guidance, it would not be possible to reopen primaries as the government planned.
He told an MPs' committee many schools would not be able to accommodate the advised 15 pupils in their classrooms.
Guidance on socially distancing in class was published on Monday evening.
It came after Prime Minister Boris Johnson said on Sunday that he hoped primary schools would re-open to pupils from Reception, Year 1 and Year 6, on June 1 "at the earliest", if infection rates and the government's other tests at the time allow it.
'Void of trust'
The guidance recommended more class sizes be cut to 15 - to allow for a two metre distance between pupils - but Mr Whiteman said many of his head teacher colleagues said they would only be able to accommodate fewer pupils in classrooms.
He told the Commons education select committee: "As we understand the requirements of social distancing today, we do not think that's possible in terms of the return that's outlined in what we've heard overnight and the day before.
The union was still getting to grips with the detail of the advice, he said which was only published late on Monday, he said.
"But," he added, "I think the real issue here is the very important bond of trust between school and family.
"School leaders and teachers are in a position that they are not quite sure of the basics of the return, and the amount of risk that's being assumed in the school setting, and all of the survey data that we are getting at the moment is that the vast majority of children's parents at the moment don't have the confidence of a return around the 1st of June."
"If we are going to fill that void, we need to understand the underpinning science, we need to understand the medical advice that goes with it so we can then determine whether it's possible in that setting or not," he added.
His views were echoed by Jenny Coles, president of the Association of Directors of Children's Services, who oversees local authority schools.
She told MPs there needed to be a lot of work locally in the communities around schools before a return to class would be feasible.
"This is not something that's going to be fixed by 1 June. It's going to take a lot of work and a lot of weeks to do that."
She said a five- or six-week lead in time was necessary to prepare parents and schools for the change.
Support around re-socialising pupils and pastoral care would be needed, and the message that had been so effective in keeping people home, would need to be reversed, so that parents felt comfortable sending their children out of their homes.
Mr Whiteman added on social distancing that individual schools were very different in terms of their buildings.
He said: "If social distancing is was we understand it, if the two metre rule is to be acted in schools, there are very many schools that simply say it's impossible to achieve 10, 12, six or even eight pupils [per class]."
Rebecca Long-Bailey, Labour's shadow education secretary, said the Department for Education guidance leaves school leaders unable to adequately plan for the reopening of their schools.
"There is still no realistic guidance for how social distancing will be kept in place with the age groups that will return first, how staff and families of children will be protected, or how class sizes of 15 will be achieved with the resources schools have."
She added that the government must urgently bring together education unions and the teaching profession to create a workable plan for the reopening of schools, when the science indicates it is safe to do so.