Boris Johnson explained why schools will not be reopened any earlier than March 8.
The Prime Minister said that the Government believed this date was the "prudent" date to begin reopening schools in England.
At the latest coronavirus briefing, Mr Johnson said that the date was three weeks after the most vulnerable groups should have received the vaccine, by which time immunity should have set in.
He said: "What we don't want to do now that we are making progress with the vaccine rollout and we have got a timetable for the way ahead, we don't want to be forced into reverse.
"We think this is the prudent and cautious approach. I think it is much better to stick to that."
Boris Johnson said NHS Test and Trace was reaching 90% of contacts.
He told a press briefing at Downing Street that it had capacity to reach 800,000 people a day, describing it as "absolutely colossal".
"Yes I do think people should self-isolate but NHS Test and Trace is reaching 90% of contacts and the vast majority of them are doing the right thing."
Chief medical officer for England Professor Chris Whitty said schools are a safe place for children to be.
Prof Whitty said it was up to ministers to decide the opening dates for schools but that he was confident the risk to children of getting Covid-19 is "incredibly low".
He said: "We consider school is a safe place for children to be as well as the right place for children to be.
"We were managing to hold the line with schools open before we got the new variant in England.
"With this new variant, which is more transmissible, we had to unfortunately do additional things which included the closure of schools to pull down incredibly high rates of increase we had up to this very high rate we've now currently got.
"The rates are now coming down but they are still incredibly high, if we were to start take-off again from the very high levels we are at the moment the NHS will get back into trouble extraordinarily fast."
Prof Whitty has emphasised that it can take several weeks for immunity to build post-vaccination.
Discussing the possibility of relaxing social distancing measures for those who have received a jab, he said: "Vaccines are going to protect in three different ways, the first of which is they are going to protect you, the person who has been vaccinated and they will protect to a very good degree based on the date we have so far."
The Prime Minister has said that the Government will set out a "route map" out of lockdown on February 22.
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He said it wasn't clear yet how far the vaccines reduce the risk of transmission, although data suggested that they probably did have an impact.
In time, he said, the vaccines would also shrink the risk from Covid-19 by reducing the amount the virus is circulating in the population, but warned: "That we are no way being close to."
He added: "The rate of virus in the community is still incredibly high so that third thing we also need to do is use the vaccine plus the social distancing that everyone is doing to pull the rate of the virus right down."
