The prime minister has insisted it was the "right thing for everybody in this country" to make sure schools in England reopen in September.
Boris Johnson's comments come after teachers, scientists, opposition politicians and the children’s commissioner for England Anne Longfield have all called for improvements to testing before pupils return in September.
One school leaders’ union said the government should have a plan B in place for schools – such as a “week-on, week-off” rota system for pupils – if there are further lockdowns and spikes in Covid-19 cases.
But speaking to reporters at a school in east London, Mr Johnson said he hoped schools would not be forced to close as a result of local action, adding it is the “last thing” that the government wants to do.
"It's not right that kids should spend more time out of school, it's much much better for their health and mental well-being, their educational prospects if everybody comes back to school, full time in September," the prime minister said.
"It's out moral duty as a country to make sure that happens."
He added that "a lot of work" behind the scenes from support bubbles to staggered start times has been put in place to make sure schools are safe to go back to.
Mr Johnson said: "The plan is there, get everybody back in September, that's the right thing for everybody in this country."
"It's the right thing for pupils, imagine, we all remember in school there is a moment where something really clicks for you, you really understand something for the first time, imagine if that wasn't happening for our kids this September?
"Imagine if they missed more of their education?"
The prime minister struck a conciliatory tone to education unions – who have raised concerns about the test and tracing system – praising the work that school staff had already done to make classrooms safe.
He said: “It’s very important that everybody works together to ensure that our schools are safe and they are – they are Covid secure – I have been very impressed by the work that the teachers have done, working with the unions, to make sure that all schools are safe to go back to in September.
“But, basically, the plan is there – get everybody back in September, that’s the right thing for everybody in this country.”
Geoff Barton, general secretary of the Association of School and College Leaders (ASCL), said heads supported the full reopening of schools in September and the pledge to make it a national priority.
But he added: “We are concerned about the lack of a national plan B if there is a second wave of coronavirus and there is a second national shutdown.
“The Government guidance requires schools to have in place their own contingency plans which are based on a return to remote education in the event of local closures.”
Mr Williamson said the government was being guided by the "best scientific and medical advice" as it boosts plans to reopen schools to all pupils in England next month.
He said: "The education and care of our children is a national priority. Ahead of the full return of all pupils to school in September, we are continuing to do everything in our power to ensure all children can be back in their classrooms safely, as this is the best place for them to be for their education, development and wellbeing."
During his schools visit, Mr Johnson said he understands the anxiety felt by pupils waiting for results after exams were cancelled and said he was "very keen" to get back to normal assessments in the coming school year.
Students have been marked based on predicted grades given by their teachers rather than the more traditional exams, which were cancelled due to coronavirus.
The system has come in for some criticism due to the lowering of grades for some individuals due to standardised weighting being applied, causing distress to some individuals.
"Clearly, because of what has happened this year, there is some anxiety about what grades pupils are going to get, and everybody understands the system that the teachers are setting the grades, then there's a standardisation system.
"We will do our best to ensure that the hard work of pupils is properly reflected."