The company said its board of directors has determined the "highly conditional" offer is not in the best interest of its shareholders. However, it did not indicate the conditions of the proposal.
"After reviewing the proposal with its financial and legal advisers, Inmet's board of directors has today notified First Quantum that it has declined to pursue the proposal," the company said in a brief statement.
Under the proposal, Inmet said First Quantum had offered $70 per share for First Quantum shares, half in cash and half in stock.
The company said the offer presented to the company Sunday followed an earlier unsolicited proposal from First Quantum of $62.50 per share.
Shares in Inmet closed up $9.20 at $62 on the Toronto Stock Exchange, while First Quantum shares were down 34 cents at $20.80.
Inmet also announced a shareholder rights plan, or so-called poison pill, a common tactic used to fend off hostile takeovers.
Its shareholder rights plan is triggered when a potential buyer acquires or announces plans to acquire 20 per cent or more of the company's shares without approval.
If a hostile deal is completed without permission, the plan gives rights holders, other than the potential buyer, the right to buy additional Inmet shares at half the prevailing market price.
Earlier this month, Inmet denied a report suggesting the company was in talks regarding the potential sale to First Quantum.
Inmet said at the time it was focused on "building shareholder value by maximizing its operating assets and through the development of its Cobre Panama copper project."
Inmet owns 80 per cent of the Cobre Panama project through Minera Panama SA and the remainder is owned by Korea Panama Mining Corp. The total cost of Cobre Panama is estimated at $6.2 billion, including $1.4 billion to be funded by Korea Panama Mining and $4.8 billion through Inmet.
Inmet, which called off a proposed merger with Lundin Mining (TSX:LUN) last year, recently dropped a hostile takeover bid of its own for Petaquilla Minerals Ltd. (TSX:PTQ) after it failed to win shareholder support.
In addition to Cobre Panama, Inmet has mines in Turkey, Spain and Finland.
The bid by First Quantum follows that sale of its operations in the Democratic Republic of Congo to Kazakhstani miner Eurasian Natural Resources Corp. for $1.25 billion.
First Quantum had written off the value of the assets in 2010 after its operations in Congo were nationalized by the government of the mineral-rich central African country.
The company has said it will focus its efforts on Zambia where it has its flagship Kansanshi mine and is developing other projects including a new mine and smelter.