Both teams were involved in the triangular series in Australia last month where England, after crushing defeats against both opponents, came from behind to defeat the hosts and reigning world champions 2-0 in the final.
With the Test sides odds-on favourites to qualify from a Group C also featuring Canada and Kenya, Friday's match has added significance.
Assuming they each do make it to the second phase, the winners of this match will carry two points forward into the Super Eights.
"We're smarting over England knocking us out in Australia and to get a good start to this tournament we have to win it, and win it well," Fleming said.
"Looking at the Super Eights you've probably got to beat every side to win this tournament at some stage and if we beat England now it may help in the long run."
England captain Michael Vaughan said recent form would count for little.
"New Zealand are a good team and are full of experience of playing in these kinds of tournaments," said the skipper.
"They are always there or thereabouts come semi-final time. We know it's a tough game for us on Friday but, as we showed in Australia, if we turn up and play we can certainly beat them."
The opening batsman, confident his hamstring will stand up to the stresses and strains of fielding for 50 overs, added: "We beat them in two different environments, in Brisbane where the ball bounced and swung a bit and in Hobart where it was a slow, Caribbean style wicket.
"We also know we lost in Adelaide."
England fell at the first hurdle during the last World Cup in South Africa four years ago but Vaughan said they were now a stronger side.
"We've got some real match-winners in this team - Andrew Flintoff, Kevin Pietersen and Paul Collingwood. These guys on any given day can win you games on their own.
"At the last World Cup, we might have had one or two match-winners. I think we've got as many as five in this team."
England's preparations suffered a set-back when fast bowler James Anderson fractured the little finger of his right bowling hand during catching practice Wednesday.
Anderson was due to have the injury re-assessed Thursday. If he isn't fit, the pace attack is likely to consist of all-rounder Andrew Flintoff, Liam Plunkett and Jon Lewis, with spin from Monty Panesar and Jamie Dalrymple.
New Zealand have injury concerns as well.
Pace bowler Mark Gillespie, who has a shoulder problem brought on by a virus, is set to miss out and opening batsman Peter Fulton is battling a finger injury.
However, big-hitting all-rounder Jacob Oram is fit after a finger problem of his own.
"We're pretty similar in our make up. We've both got good left arm spinners (New Zealand have Daniel Vettori), the all-rounder sides of things is taken care off with Jacob and Flintoff," said Fleming.
However, Fleming said there was an area where he thought his side had the advantage.
"One thing we've got maybe is experience, we have some pretty experienced players in our side. The English have played a lot of county and domestic cricket but in internationals and World Cups I think we've got them covered."
Both England coach Duncan Fletcher and New Zealand counterpart John Bracewell were at Beausejour for Wednesday's opening group match between Canada and Kenya as they assesed the conditions.
"My quick assessment (New Zealand spent some time at the ground on Tuesday) was it is going to be slow," said Fleming. "How much turn there is will be interesting keeping in mind the quality of the spinners on show Friday."
New Zealand: Stephen Fleming (capt), Shane Bond, James Franklin, Peter Fulton, Mark Gillespie, Michael Mason, Brendon McCullum (wk0, Craig McMillan, Jacob Oram, Jeetan Patel, Scott Styris, Ross Taylor, Daryl Tuffey, Daniel Vettori and Lou Vincent. Coach: John Bracewell.
England: Michael Vaughan (capt), James Anderson, Ian Bell, Ravi Bopara, Paul Collingwood, James Dalrymple, Andrew Flintoff, Ed Joyce, Jon Lewis, Sajid Mahmood, Paul Nixon (wk), Monty Panesar, Kevin Pietersen, Liam Plunkett and Andrew Strauss. Coach: Duncun Fletcher.