The West Indies Cricket Board said nine players took up its offer, reports the Sydney Morning Herald.
Selectors were to meet on Wednesday to invite new players to a training camp from November 29.
The board didn't specify which players had responded.
The spat arose after some players signed personal contracts with a rival of the team's new sponsor.
Board spokesman Leonard Robertson said on Monday that vice-captain Ramnaresh Sarwan, Chris Gayle and Dwayne Bravo were the main protagonists, and that captain Brian Lara might join them.
In a statement issued on Tuesday, Robertson said: "The players who didn't accept the invitation ruled themselves out of consideration for this tour. This doesn't prevent them from being considered in the future should they merit inclusion."
Negotiations between the board and players' representatives broke down last Friday after 14 hours of talks.
The West Indies Players' Association asked players not to sign the contract because it infringed their commercial rights.
Telecommunications company Digicel in July agreed to pay about $20million to sponsor the team for five years. Cable and Wireless, the previous sponsor, responded by signing eight players to individual deals.
