"The coronavirus could be with us for a year or more" so children cannot continue to stay out of school for "months and months" longer, says Education Secretary Gavin Williamson.
But he told BBC Breakfast he recognised there would be "initial nervousness" among parents about children returning.
Teachers' unions have warned it is not safe to open England's primary schools on 1 June.
On Sunday, Boris Johnson accepted some schools would not be ready to open.
The education secretary said the first steps for returning to school had to begin.
"We cannot be in a situation where we go for months and months where children are missing out on education," said Mr Williamson.
Challenged over whether the row over Dominic Cummings had undermined the credibility of the government's health advice, he said "safety was at the heart" of planning for pupils to return.
This has not persuaded teachers' unions - with no sign of a resolution to the stand-off over bringing increasing numbers of children into schools.
Geoff Barton, leader of the ASCL head teachers' union, said the government had "not done a good job in building confidence in its plans".
Ministers were failing to win "trust and confidence", said Patrick Roach, leader of the Nasuwt teachers' union.
Mr Williamson told BBC Breakfast that he recognised there would be hesitation among parents.
"We do realise there will be an initial nervousness about the return of schools," he said.
And he said it was right that there would be no penalties for parents who decided to keep children at home.
Asked whether parents should now rely on their "instincts" rather than official guidance, he said he hoped that parents would start to send their children back to school.
He said the guidance for returning to school ensured a "maximum amount of safety" - and going back would be important for children's well-being as well as helping them to catch up on lost lessons.
Schools have remained open for the children of key workers and vulnerable children - and the government's plan is for all pupils in Reception, Year 1 and Year 6 to return to school from 1 June.
But many local authorities have already indicated that their schools will not be ready to open, or that schools will have their own variations on which pupils will return.
Mr Williamson said there was no reason why most schools should not open - but gave no indication of any sanctions for those that did not.
The first children returning to secondary school, in Years 10 and 12, will begin on 15 June.
School leaders have questioned the feasibility of the next stage of reopening, which would have all primary children back in school together for the last month of term.
The Department for Education says this part of the plan is now "under review".
Schools in Wales will not go back on 1 June, but a date has not yet been set.