Johnson also confirmed that the government was looking at a Covid-19 status certification system, or vaccine passport, to help reopen larger events and to travel.
However, with many countries across Europe suffering a third wave of COVID infections, the government has not yet been able to confirm whether foreign holidays will be allowed beyond that date - leaving many families uncertain whether to book a summer break overseas.
"Obviously we are hopeful that we can get going from May 17th, but I do not wish to give hostages to fortune or to underestimate the difficulties that we are seeing in some of the destination countries that people might want to go to", he said.
Virgin Atlantic chief executive Shai Weiss told reporters that the Government must aim to enable people to return from "green" countries without the need for tests.
The prime minister also responded to a call from the boss of easyJet to allow people to use lateral flow tests - rather than more expensive PCR tests - as part of border requirements when returning from overseas.
No isolation would be necessary on return to the United Kingdom from green countries, but pre-departure and post-arrival tests would be required, potentially costing up to £200 each.
Countries on the amber list would require self-isolation. "We're going to see what we can do to make things as flexible and as affordable as possible".
He insisted he does "want to see global travel start up again" but said hopeful holidaymakers should be "realistic" because "a lot of the destinations that we want to go to at the moment are suffering a new wave of the illness".
"We can't do it immediately, but that doesn't mean we've given up on 17 May". We can't do it immediately, but that doesn't mean we've given up on May 17, when we'll be saying as much as we can as soon as we can about worldwide travel.
"I wish I could give you more on that, I know that people watching will want to know exactly what they can do from May 17, but we're not there yet", Johnson said. "Where we hoped confidence would start to pick up, and more people would be interested in booking holidays... that just won't come this week".
Mr Johnson has already announced that, from Friday, everyone in England will be able to access free lateral flow tests twice a week as a means of helping to prevent new outbreaks.
EasyJet CEO Johan Lundgren said on Tuesday that there were a lot of details missing from the previous day's announcement.
He said the cost of Covid-19 tests sometimes exceeded easyJet's ticket prices.
However, speaking on a visit to AstraZeneca laboratory in Macclesfield on Tuesday, Mr Johnson said: "I do want to see worldwide travel start up again".
"That doesn't make sense for me. because this could add to cost and complexities", he told BBC Radio. If you think you have the virus, don't go to the GP or hospital, stay indoors and get advice online.
Stay alert to stop coronavirus spreading - here is the latest government guidance. Only call NHS 111 if you can not cope with your symptoms at home; your condition gets worse; or your symptoms do not get better after seven days. In Scotland anyone with symptoms is advised to self-isolate for seven days.