It was "not fair to have our name associated with that bat", Mr Laver said.
New Balance has its bats made by suppliers in India and England, the company said.
Mr Laver said many of his company's bats were being used during the World Cup but contractual arrangements meant he was not at liberty to say which players were using them.
"It's one of those things that we can't actually say what we do," Mr Laver said. "We do a lot of work with guys who play international cricket but they are all contracted to other brands."
When pressed on Elliott's bat, Mr Laver said it was "not fair to have our name associated with that bat".
Most big brand cricket bats were made under contract by a variety of manufacturers, Mr Laver said.
"There just aren't genuine batmakers that do the whole hog themselves these days. We've sort of become quite unique because we don't use international players and sponsorship as a means of selling.
"We use the process of making our bats and the way we deal with our customers - it's the whole bespoke, custom-made concept that sells our product."
Business is booming for the seven-man operation, which was founded in 1999 and now makes around 1200 bats a year.
"It is taking a bit of a leap forward at the moment," Mr Laver said. "The last year has been really good. It's a really exciting time. Being based in New Zealand, we have been trying to create a really good name for ourselves and that appears to be happening; 90 per cent of our sales are overseas."
"This is gold for us, it really is. What we have always struggled with, to a degree, is that we are based in New Zealand, but New Zealand hasn't always been in the top ranks of cricket worldwide ... So this is fantastic for us. It really couldn't come at a better time. It just helps to give us credibility."
CORRECTION: The original version of this story has been amended to clarify that Grant Elliott's bat was made under contract for New Balance in India, not by Laver & Wood.
