Schools minister Nick Gibb revealed kids in Years two, three, four and five who are not going back on Monday may be brought back in split classes.
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Groups would be brought in on alternate weeks in small schools where social distancing is not possible.
A similar approach for pupils going back to school next Monday was recommended by the government’s SAGE group of scientists, but was ruled out to give kids a more “consistent”education.
Asked about bringing in more year groups back to school at the Education Select Committee, Mr Gibb said: "We are looking at all the different options, for example rotas, for those at that stage.”
The minister added: "That is one of many possibilities of how we bring back more children while maintaining social distancing.”
It will not apply to groups coming back on Monday.
He revealed ministers had rejected proposals to have children come back to school on a rota basis.
Department of Education chiefs rejected plans for children to come back into classrooms in a two week on, two week off rota.
He said “It is better for children to have full time education consistently.”
He added the proposal which had been suggested by the SAGE group of government scientists had been thrown out as it did not consider parents' ability to work.
Schools will only open if the R rate is continuing to decrease.
Mr Gibb added: “We will be totally led by the science – we don't know for certain that schools will return on the first of June for reception, year one and year six.
“That will depend on the science, although schools are planning for it and all the indications are that the science is moving in the right direction but the confirmation of that will be tomorrow.
“So we don't know until we see more evidence of R factor continuing to reduce over the next few weeks.”
He also revealed that more than a million children on free school meals will get £15 vouchers over the half term break after a Government u-turn on the policy this morning.
The scheme, which was introduced over the Easter break would be extended to help more than 1.3 million kids.
Mr Gibb said the free school meal vouchers scheme had had a "bumpy start in terms of the software and how you applied for the vouchers" but that £101m of vouchers had been redeemed in supermarkets so far.
He said: "The cost of the voucher scheme will continue to be met by the Department for Education over half term."