It is still not decided whether or not all primary children will really be asked back to school next month, schools minister Nick Gibb told MPs.
After the first wave of pupils return on 1 June in England, ministers aim for all primary year groups to go back for four weeks before the end of term.
Mr Gibb was pressed by MPs on the education select committee whether this full return in mid-June was "unlikely".
"It is difficult to say," the minister told the select committee.
The minister for school standards was challenged by MPs about whether plans to bring all primary year groups back into school for the last month of term were still going ahead.
"Is it unlikely that the government's ambition for all children in primary school to return before the summer is going to happen?" asked committee chair, Robert Halfon.
"I think you need to give some steer," Mr Halfon urged the minister.
"It is difficult to say. It will be totally led by the science," said Mr Gibb.
He told MPs the decision - which would mean more than another two million children returning to primary school - would depend on the level of coronavirus infection over the "next few weeks".
Head teachers, uncertain about what they should be planning, have questioned the plausibility of accommodating all years in primary school, when they will be limited to 15 pupils per classroom.
Committee member Christian Wakeford MP said that in some schools there was "literally no room" for that to be done safely.
The minister suggested there could be a rota system - but also spoke of the importance of full-time lessons so that parents would be able to go to work.
"It's better for children to have full-time education consistently, " he told MPs.
Mr Gibb was challenged over whether the row over Dominic Cummings had damaged the credibility of the government's health messages - which could reduce trust in the safety of returning to school.
"The government's message has been undermined - and even though the law may not have been broken, the spirit of the law has indeed been broken," said Conservative MP Jonathan Gullis.
He asked how the Department for Education could "rebuild and regain confidence".
Mr Gibb said that: "The reason we can even have this discussion is because of the success of people's commitment to social distancing."
He told MPs: "The more we all adhere to the rules the more that we'll be able to make further progress in reopening schools."