In a letter sent to ConsMin's share registry today, Kiernan asked shareholders in the company to contact the ConsMin board and demand it delay the meeting on the private equity offer from the consortium headed by Brian Gilbertson's Pallinghurst Resources.
Kiernan said that delaying the meeting would give shareholders time to evaluate Territory's alternative offer, should it decide to make one.
Territory has so far only released an alternative proposal for acquiring the manganese miner and plans to decide on July 16 whether or not to make an alternative bid.
ConsMin shareholders are scheduled to vote on whether to accept Pallinghurst's bid on July 19.
The ConsMin board has recommended they accept the Pallinghurst offer, which is currently at $1.68 a share plus two shares in a ‘new' ConsMin for every five shareholders held.
The Pallinghurst bid is led by ex-BHP chief Brain Gilbertson and has the backing of private coal miner AMCI and banking group Investec.
In today's letter, Kiernan, who was ConsMin's managing director for eight years until last June, reiterated Territory's alternative proposal.
The Perth-based company put forward two revised options last week, the first for either $2 in cash for every ConsMin share, plus one share in Territory, which were last trading at $1.14 after shedding 2.5c in morning trade. The second offer is three Territory shares for every one of ConsMin's, currently worth about $3.43.
Kiernan said that Territory's proposal, which is not yet an official offer, valued the company higher than the Pallinghurst bid.
The proposal from Territory has the backing of commodity trading houses Noble Group and DCM Decometal and US investment bank Lehmann Brothers.
Territory is conducting due diligence, which it will complete tomorrow.
Shares in Consolidated Minerals were last trading up 1c at $3.08.