Britain's Sunday Times newspaper said Oceania Football Confederation (OFC) president Temarii and Nigeria's Amos Adamu - both members of world football governing body FIFA's executive committee - had offered to sell their votes when approached by reporters posing as lobbyists for an American consortium.
The newspaper report said Adamu was filmed asking for 500,000 pounds for a personal project and that Tahitian Temarii asked an undercover reporter in Auckland for NZ$3m ($2.27 million) to fund a sports academy at the OFC's headquarters.
"Further to information made public by The Sunday Times, the OFC President and FIFA Vice President Reynald Temarii will cooperate fully with the FIFA Ethics Committee and the FIFA Secretary General," a statement from the OFC said.
"Reynald Temarii welcomes a full and thorough investigation so that all the facts can be heard."
The OFC said it would not comment further until the findings of the FIFA Ethics Committee have been released.
FIFA will decide on December 2 in Zurich which countries will host the 2018 and 2022 World Cups. The choices will be made by the 24-strong executive committee.
"UNPLEASANT SITUATION"
However a source close to the executive, who asked not to be named, said both Adamu and Temarii could find themselves suspended or off the committee by then if the claims against them were substantiated.
"FIFA will not allow anyone or anything to damage the reputation of the voting procedure and it could be that 22 men might make the decision, not 24," the source said.
England and Russia are bidding for the 2018 finals along with joint bids from Spain/Portugal and Belgium/Netherlands. The candidates for 2022 are the United States, Japan, South Korea, Qatar and Australia.
FIFA president Sepp Blatter appealed to his executive committee members to stay silent as he launched an investigation.
"I am sorry to have to inform you of a very unpleasant situation which has developed in relation to an article published... in the Sunday Times, entitled 'World Cup votes for sale'," Blatter wrote at www.fifa.com.
"I will keep you duly informed of any further developments. In the meantime, I would like to ask you to refrain from making any public comments on this matter."
