The Black Caps - like defending champions Australia unbeaten at the tournament so far - top the Super Eights table on run-rate.
But unlike Australia, who've beaten South Africa, and are chasing an unprecedented third straight title, they've yet to come up against a leading one-day international side at this event although they did defeat England by six wickets in their opening group match.
One more victory will see New Zealand, yet to win the World Cup, into the last four.
Thursday's match marks the start of a run of games that sees them up against 1996 champions Sri Lanka, South Africa and Australia in the space of 10 days in Grenada.
"We know we are capable of winning it," said Fleming.
But all-rounder Jacob Oram added: "These three games will either build on our confidence or chip away at it."
New Zealand are now just one short of equalling their 10-match winning run of 2004, having already beaten Australia three times at home before coming to the Caribbean.
However, Sri Lanka captain Mahela Jayawardene for one believes New Zealand have yet to be tested at this tournament.
"They are playing some really good cricket but they haven't played one of the top teams yet," he told AFP.
Hosts New Zealand, third in the International Cricket Council (ICC) one-day ratings, and fourth-placed Sri Lanka squared a five-match series 2-2 in January after the final game was washed out.
But the balance of Thursday's match could swing New Zealand's way before a ball is bowled if Lasith Malinga is ruled out.
Sri Lanka's fast bowling ace missed practice Tuesday after sustaining ligament damage in his left ankle during an earlier training session.
Malinga, whose round-arm action makes him difficult to face - New Zealand asked umpires to put sweaters round their waists to act as an additional sightscreen last time they played against him - tops the tournament bowling averages with 15 wickets at an average of under 15.
And against South Africa his record-breaking four wickets in four balls so nearly saw Sri Lanka to a stunning win.
"Lasith has an ankle problem and we'll assess it over the next couple of days. We're not sure he's 100 percent," Jayawardene explained.
Farveez Maharoof and Nuwan Kulasekara, the most likely replacements, don't spook opponents as much as Malinga.
But last time out unheralded quick Dilhara Fernando saw Sri Lanka to a two-run win over England by clean bowling Ravi Bopara last ball.
And their attack will still include left-arm quick Chaminda Vaas and incomparable off-spinner Muttiah Muralitharan, both World Cup winners.
Sri Lanka's two most recent one-day wins against New Zealand featured major contributions from opener Sanath Jayasuriya - 111 in Napier and 70 in Auckland.
One criticism of Sri Lanka is that they are too often dependent on the veteran left-hander for big scores.
But Jayawardene said generally slow West Indian surfaces meant ideas of good totals had to be revised.
"On these pitches 230, 250 is a very acceptable score. Sanath didn't get many against England (25) but the middle-order did well."
New Zealand bat a long way down, Oram and fellow all-rounder Scott Styris pivotal figures, while a well-balanced attack features fast bowler Shane Bond and left-arm spinner Daniel Vettori.
"They've got guys who can bail them out if they struggle at the top. But we've played them a lot in the last 12 months and we know their strengths and weaknesses," said Jayawardene.
New Zealand must decide whether to recall batsman Ross Taylor, whose 128 in Napier, was his maiden one-day international hundred.
Taylor has missed the last four games due a hamstring injury, sustained during his half-century against Kenya in a group match.
Sri Lanka: Mahela Jayawardene (capt), Kumar Sangakkara, Sanath Jayasuriya, Upul Tharanga, Marvan Atapattu, Tillakaratne Dilshan, Russel Arnold, Chamara Silva, Chaminda Vaas, Farveez Maharoof, Lasith Malinga, Dilhara Fernando, Nuwan Kulasekara, Muttiah Muralitharan and Malinga Bandara. Coach: Tom Moody.
New Zealand: Stephen Fleming (capt), Shane Bond, James Franklin, Peter Fulton, Mark Gillespie, Michael Mason, Brendon McCullum, Craig McMillan, Jacob Oram, Jeetan Patel, Scott Styris, Ross Taylor, Daryl Tuffey, Daniel Vettori, Hamish Marshall. Coach: John Bracewell.