Boris Johnson is examining whether some lockdown measures could be lifted once the highest priority groups have been vaccinated as he came under pressure to reopen England's schools.
The Prime Minister said the Government was "looking at the potential of relaxing some measures" but refused to guarantee that pupils would return to classes before Easter.
His comments come as a surprise as Health Secretary Matt Hancock suggested on Sunday any relaxation was a "long, long way" off.
Speaking to reporters on a visit to a vaccination site at Barnet Football Club in north London, Mr Johnson said ministers were looking at infection rates and progress in vaccinating the top priority groups, which are expected to be completed by mid-February.
"But before then we'll be looking at the potential of relaxing some measures," he said.
Downing Street aides insisted Mr Johnson meant February 15 was the earliest point at which any of the rules could be changed, not before.
Mr Johnson stressed he would not do anything that could risk a surge in cases as he declined to commit to a timetable for the return of schools.
"I do think now this massive achievement has been made of rolling out this vaccination programme, I think people want to see us making sure we don't throw that away by having a premature relaxation and then another big surge of infection," he said.
"I totally understand the frustrations of parents, I really thank teachers for what they're doing, the immense efforts they're going to to teach kids online and the Government has provided a lot of laptops ... I know that's no substitute for direct face-to-face learning.
"Believe me, there's nothing I want to do more than reopen schools, I've fought to keep schools open for as long as I possibly could.
"We want to see schools back as fast as possible, we want to do that in a way that is consistent with fighting the epidemic and keeping the infection rate down."
Mr Johnson's comments came as he faced pressure from senior Tories to allow pupils to return to class.
Education Secretary Gavin Williamson is widely expected to confirm this week that there will be no return to the classroom after the February half-term break as ministers had hoped.
Robert Halfon, Tory chairman of the Commons Education Committee, called for action to get pupils back in classes amid mounting Tory unrest about the Government's exit strategy from coronavirus restrictions.
Mr Halfon told the BBC: "It may be that one thing the Government should consider is that even if there are tighter restrictions in other parts of our society and economy, you have those restrictions in order to enable the schools to open."
He has called for a minister to be summoned to the House of Commons to explain the Government's approach.
Mr Halfon hit out at ministers for placing a lower priority on children's education than the economy.
"I want the engine of Government to be directed towards opening our schools again," Mr Halfon told Times Radio.
"For the Government to place as much importance on schools and colleges as they do on the economy and the National Health Service."
Meanwhile, senior ministers are due to meet on Tuesday to discuss a proposal to require travellers arriving in the UK to pay to quarantine at a designated hotel to ensure they are following the rules on self-isolating.
Mr Johnson said: "We have to realise there is at least the theoretical risk of a new variant that is a vaccine-busting variant coming in, we've got to be able to keep that under control."
He said "that idea of looking at hotels is certainly one thing we're actively now working on".
"We need a solution that gives us the maximum possible protection against reinfection from abroad."
The pressure on Mr Johnson and Mr Williamson over schools is just one aspect of the wider unease on the Tory benches about the Government's strategy.
Former chief whip Mark Harper, chairman of the Covid Recovery Group – made up of lockdown-sceptic Conservative MPs – again called for an early March easing of restrictions.
He told BBC Radio 4's Today programme that two or three weeks after the four priority groups have been vaccinated lockdown measures should start being lifted.
"At that point you need to start bringing the economy back to life and the first thing that needs to be reopened are our schools so our children can get back, mix with their friends and enable their education and their social development to take place," Mr Harper said.
"What we are asking for now is the Government to set out that plan and bring some clarity."
The latest Government figures showed more than 6.3 million people across the UK have received their first dose of the vaccine – with a record-breaking 491,970 being injected in a single day over the weekend.
Based on the latest figures, an average of 393,031 first doses of vaccine would be needed each day in order to meet the Government's target of vaccinating the top four priority groups – including all over-70s – by mid-February.