Education Secretary Gavin Williamson has said he cannot give a date for when schools will reopen following reports children could be back in the classroom in just three weeks.
Mr Williamson said he wanted "nothing more" than to see children return to school but warned any relaxing of the coronavirus lockdown measures could only be taken when five key tests have been met.
It came after Michael Gove denied suggestions the Government had drawn up plans for a three-tiered relaxation of restrictions.
The reports claimed a "traffic light" strategy was about to be brought in which would see some schools and businesses allowed to reopen in mid-May.
Speaking at the daily Downing Street press conference, Mr Williamson said: "People are anxious to know when we're going to relax restrictions, when schools are likely to be fully back and open again.
"Of course, I want nothing more than to see schools back, get them back to normal, make sure the children are sat around learning, and experiencing the joy of being at school.
"But I can't give you a date. Because before we do, we need to meet five tests."
The Education Secretary reiterated the five tests first outlined by Dominic Raab on Thursday, which include protecting the NHS's ability to cope, ensuring a drop in the daily death rates and having reliable data to show the rate of infection is decreasing to manageable levels.
The Government must also ensure sufficient testing capacity and PPE supplies, and be confident any change in the measures will not risk a second peak of infections, Mr Williamson said.
"When we can be sure that we have met these five essential points, we can think about getting children into schools again, learning, mastering new ideas and being with their friends once more," he added.
The number of deaths in hospitals in the UK has now topped 16,000, with thousands more expected in care homes.
The Department of Health said a total of 16,060 had died in hospitals as of 5pm on Saturday, up by 596 from the day before.
Meanwhile, Mr Gove defended the Prime Minister for not attending five meetings of the key Government Cobra committee in the build-up to the coronavirus outbreak.
A wide-ranging report in The Sunday Times stated a number of opportunities were missed by the Government in January, February and March to try to lessen the impact of the gathering crisis.
Speaking on Sky News's Sophy Ridge On Sunday programme, Mr Gove said: "The idea that the Prime Minister skipped meetings that were vital to our response to the coronavirus, I think is grotesque."
The long-time ally of Mr Johnson later told BBC One's The Andrew Marr Show that "most Cobra meetings don't have the Prime Minister attending them".
In other developments on Sunday:
– A delivery of 84 tonnes of personal protective equipment (PPE) for frontline workers due to arrive in the UK from Turkey on Sunday was delayed;
– Sir Jeremy Farrar, a member of the Government's Scientific Advisory Group for Emergencies (Sage), said he is "optimistic" about finding a vaccine for Covid-19;
– Professor Sarah Gilbert, professor of vaccinology at Oxford University, who is leading a team developing a Covid-19 vaccine, said nobody can be sure it is possible to find a workable vaccine, but the prospects are "very good";
– Scottish Health Secretary Jeane Freeman announced that an emergency hospital in Glasgow, named the NHS Louisa Jordan, will be ready to receive patients from Monday;
– A decision on whether Nazanin Zaghari-Ratcliffe's temporary release from a prison in Iran will be extended was delayed again;
– Mr Gove reiterated the Government will meet its 100,000 daily testing target by the end of the month;
– The Cabinet Office Minister also said Mr Johnson is "in cheerful spirits" as he continued his recovery from coronavirus;
– The fundraising campaign for 99-year-old Captain Tom Moore passed £26 million in donations.