''The Irish are a very good team and throughout the tournament even their defeats are also very graceful. They have been playing wonderful cricket and we can not allow them any room to manouever,'' Flemming told reporters after the morning work out.
Ireland, on the other hand, are drawing inspiration from the superlative performance by Bangladesh on Saturday at the same ground.
Coach Adrian Birrell was in the Providence stadium for most part of the second session to see the sensational win.
The Black Caps and Australia are the two teams who so far remain unbeaten in the World Cup.
But Fleming does not want any competition. ''Frankly speaking we do not want them to give us a tight match. They are good but we are better. The minnows have always added advantage in a tight match because you carry the extra pressure,'' he said.
Ireland, still smarting from successive defeats, will like to turn it around for one last time. But a hamstring injury sustained during training has put all-rounder Andre Botha's availability in doubt for the game.
''The next 24 hours are crucial,'' Ian Knox, team physio, said as Ireland await details of the extent of Botha's injury.
''We do hope that he will be back an we are keeping our fingers crossed,'' said Birrell.
Kevin O'Brien is likely to return to the side, while brothers John and Paul Mooney are standing by for Botha.
Meanwhile, Ireland received a good luck message from the Duke of York, who met team officials during a visit to Guyana.
''I've been following the competition on the television, and like everyone else I'm delighted that you have reached the Super Eight phase and hopefully you'll pull off another memorable victory,'' the Duke said.
New Zealand have been tipped by many, including Ian Chappell and Sir Viv Richards, to make it to the final of the tournament.
Captain Fleming looked at the side's success so far as a 'very satisfying, experience and was confident they would go all the way.
''One of our strengths is that we bat low down and we're strong in the last ten overs and I think that will become prevalent in the last few games of the tournament,'' said Fleming.
''The thing about our game so far is that we haven't relied on one person. Some teams rely on one or two players and you know that if you put them under pressure then the rest of the side is under pressure.
The strength for New Zealand is that we have guys from one to 11, who are fit and raring to go, and on his day win a game,'' he added.
Eire seek motivation from Bangla: Ireland captain Trent Johnston believes Bangladesh's shock win over South Africa can inspire his side when they take on high flying Kiwis in their World Cup Super Eights tie.
"It (Bangladesh win) has given us probably some motivation to compete with these bigger teams," said Johnston of lowly-ranked Bangladesh's surprising 67-run defeat of Graeme Smith's men here on Saturday.
Johnston said Bangladesh's win was set up by their spinners.
"We watched the match and Bangladesh performed fantastically well and their three spinners are crucial to their plans and set up the win. It's (playing spinners) probably one area that we need to work hard on in the middle overs."
Bangladesh, who set South Africa a target of 252 to win after being put into bat, were spurred on by their three left-arm slow bowlers who shared six wickets between them to shoot their opponents out for just 184.
While Bangladesh now fancy their outside chances of a place in the semi-finals, Johnston's men still in search of elusive first win in Super Eights round.
When asked if Bangladesh's win put pressure on Ireland to make their presence felt, Johnston replied: "I don't think so, Bangaldesh play a lot more cricket than us and have more experience.
"We would like to finish seventh rather than eighth (in the table) but for that we have to work hard. We will play Bangladesh (Apr 15) and will focus on what we can do," said Johnston.
Ireland meet defending champions Australia (Apr 13), Bangladesh (Apr 15) and Sri Lanka (April 18) in their remaining matches.
Johnston said that not being able to repeat the performance which shocked Pakistan had been disappointing.
"If we are going to beat (another) big team we are going to have to play out of our skins and they are going to have a bad day," Johnston added. "We are capable of playing out of our skins."
New Zealand: Stephen Fleming (capt), Shane Bond, James Franklin, Peter Fulton, Mark Gillespie, Michael Mason, Brendon McCullum (wk), Craig McMillan, Jacob Oram, Jeetan Patel, Scott Styris, Ross Taylor, Daryl Tuffey, Daniel Vettori and Hamish Marshall. Coach: John Bracewell.
Ireland: Trent Johnston (capt), Kyle McCallan, Andre Botha, Jeremy Bray, Kenneth Carroll, Peter Gillespie, Dave Langford-Smith, John Mooney, Paul Mooney, Eoin Morgan, Kevin O'Brien, Niall O'Brien (wk), William Porterfield, Boyd Rankin and Andrew White. Coach: Andrew Birrell.