Mr Peters said the claims were "palpably untrue" and that Dr Sharples was trying to "impugn my integrity and suggest I was a hypocrite".
Mr Tamihere said he would not comment about employees or consultants on grounds of privacy.
The Maori Party co-leaders made the claims after Mr Peters criticised a $6 million Whanau Integration, Innovation and Engagement Fund, claiming it effectively funded family reunions.
Yesterday, Mr Peters continued his attack, questioning Prime Minister John Key about the accountability of the scheme and whether money could be tracked after a provider received it. Mr Key said all Government spending was closely watched and accountable to the public.
Whanau Ora Minister Tariana Turia said Mr Peters' attacks were scurrilous. "We are talking about a person who in his previous time in Parliament took $158,000 worth of taxpayers' money and never ever paid it back. Mr Peters knows nothing, and he shouldn't keep guessing."
NZ First had given $158,000 to charity after the party was found to have unlawfully spent that amount of Parliamentary Services money during the 2005 campaign. Other parties had repaid Parliamentary Services.
Mrs Turia said Whanau Ora funding was closely monitored. A review was due to start soon.
Meanwhile, Whanau Ora was also the subject of more Labour accusations of political interference in NZ on Air.
Labour broadcasting spokeswoman Clare Curran released documents showing NZ on Air board member Stephen McElrea was one of four people on a subcommittee that selected four documentaries to fund - including one on Whanau Ora. Mr McElrea is Mr Key's electorate chair and an office holder in National.
Labour has previously criticised Mr McElrea for raising concerns about a NZ on Air-funded documentary on poverty screened before the election.