Casting the referendum as “a vote for your life”, the Prime Minister said young people still had until June 7 to sign up for a vote in the June 23 poll.
And he signalled he is ready to accept the slenderest of majorities as a victory for Remain, dismissing the argument that a close result could provide the platform for a swift re-run poll.
Ukip leader Nigel Farage argued anything short of a two-thirds majority for Remain would represent “unfinished business” and could provoke demands for an early second referendum from Leave advocates who feel the campaign has not been run fairly.
But Cameron said it was “obvious” a simple majority was enough to settle the question in a referendum and Brexit supporters had to stick to the rules.
Speaking during a visit to Japan for the G7 summit, Cameron said: “There are very clear rules for referendums - you’ve got to get out there and win a majority.”
Cameron made no effort to conceal his anxiety that younger voters - who polls suggest are strongly in favour of continued EU membership - may not use their ballots on June 23.
Some pollsters believe a low turnout among the young is the most likely factor to produce victory for Brexit, which is more popular among older age groups.
“One thing on the campaigning front that is probably my greatest concern is doing everything we can in the next week to get people to register to vote, particularly young people,” said the Prime Minister.
“This is absolutely a vote about their future. This vote will determine the sort of country, the sort of economy they grow up in, the sort of opportunities that they have.
“Definitely something that is concerning me is that the last election turnout among young people was more in the 40 percents rather than the 60 percents.