Anglo American on Wednesday said it had rejected an improved and final takeover offer from rival mining group BHP worth £38.6 billion (R892bn).
"The board of Anglo American has unanimously rejected the latest proposal," a statement said regarding the third offer.
However, it added that it is "willing to continue to engage with BHP and its advisers".
In a separate statement, BHP CEO Mike Henry said his company "has put forward a final offer", which represented "a significant increase from" the first bid.
The second offer had been worth £34bn, up from an initial bid of £31.1bn in April.
Following rejection of the second bid earlier this month, Anglo announced it would offload its coal, diamond and platinum businesses to focus on critical minerals.
BHP has hoped to create a copper titan by purchasing Anglo.
Copper is essential to the world's transition to renewable energy because it is a vital component for greener technology like energy storage, electric vehicles, solar panels and wind turbines.
The price of copper has soared over the past year as a result and Anglo American expects the trend to continue.
Anglo American was founded in South Africa in 1917 by the German-born industrialist Ernest Oppenheimer, 15 years after his arrival in the country.
It is now one of the largest mining companies in the world and is listed on stock exchanges both in London, where it is based, and Johannesburg.
BHP's offer, which proposed Anglo American hiving off its platinum and iron ore production activities in South Africa, caused a stir in South Africa just before the tightest general election in decades.
Some analysts and opposition politicians viewed such a proposal as an indictment of the decline of South Africa's mining sector and how foreign investors see the country.
AFP