The Prime Minister said he hoped to give more information about foreign travel on April 5, a week before the Government's global travel task force is due to report.
"A lot of people do want to know about what's going to happen on the holiday front and I know there's a great deal of curiosity and interest," Mr Johnson said at a No 10 press conference.
"All I can say is it's just too early to say and my advice is to everybody to wait for the global travel task force to report.
"We've heard already that there are other European countries where the disease is now rising so things certainly look difficult for the time being but we will be able to say more we hope in a few days' time, I certainly hope to say more by April 5."
Under the current road map for easing restrictions, the earliest date people in England could go on holiday abroad would be May 17.
A senior scientific adviser has suggested people should plan to holiday in the UK this summer.
Professor Neil Ferguson, whose modelling led to the first UK lockdown last March, said relaxing border measures too early risked the success of the UK's vaccination programme.
He said the risk from Europe is the arrival of new variants, or importing cases of the troubling South African variant from countries where cases were rising.
He told BBC Radio 4's World at One programme: "I should say we also have some of the South African variant here already and other variants which may be similar, which we're watching very carefully, so that is overall the major concern going forward and why we need to be vigilant, not just looking at Europe, and what's happening within our borders as well."
Prof Ferguson said the effectiveness of the AstraZeneca and Pfizer vaccines "might drop substantially, 60% or 50%" in the face of variants.
"And what that means is if we then allow transmission to resume which it is likely to do as we relax social distancing measures, we have that faint risk of being back in a situation where we have rising infections, rising hospitalisations with people who have been vaccinated," he said.
"And back to, in the worst case, where we were in January."
Asked if he was therefore in favour of keeping borders closed, Prof Ferguson said: "I certainly am in favour of relaxing border measures at a slower rate than we relax controls within the country, and doing all we can to reduce the risk of importation of variants which might undermine our vaccination programme."
Asked what he wanted to see, he said that meant having finished "vaccinating everybody under 50, which will be late summer, and having vaccines in our stockpile which we know work very effectively against those variants".
"Conservatively and being risk averse at the moment, I think we should be planning on summer holidays in the UK, not overseas."
He said most people travelling to and from France at the moment on essential business or for commerce were exempt from quarantine and testing measures.
Reporting by PA