Anglo American has rejected calls from the rival mining company BHP to extend its deadline for takeover talks for a potential deal worth almost £39bn.

The companies have been in discussions over a deal worth almost £39bn since Anglo rejected BHP’s third improved offer a week ago amid efforts to come to an agreement on the structure for a potential takeover.

Australia’s BHP has a deadline until 5pm on Wednesday to make a final offer or walk away from takeover talks for at least six months.

Anglo American said in a statement that BHP “has not addressed the board’s fundamental concerns relating to the disproportionate execution risk associated with the proposed structure”.

It said that after discussion with shareholders it had concluded that there was no basis for a further extension to the deadline for the “highly complex and unattractive structure”.

BHP’s three takeover approaches over the past five weeks all had a requirement for its rival to spin off its South African operations, resulting in heavy criticism from the government in Pretoria. Anglo American had opposed this.

However, Anglo has proposed its own corporate shake-up, including a pledge to break up the 107-year-old business and sell its platinum division and its De Beers diamond arm, in a plan that has the backing of the South African government.

In a statement on Wednesday, BHP said: “BHP believes that the proposed measures it has put forward provide substantial risk protection for Anglo American shareholders and supplement the significant value uplift that Anglo American shareholders will receive from the potential combination.

“BHP believes a further extension of the deadline is required to allow for further engagement on its proposal.

“This announcement does not amount to a firm intention to make an offer and there can be no certainty that an offer will be made.”

A mega-merger between the two companies would have created the biggest copper miner in the world, with 10% of global output.

Anglo American’s vast reserves of copper are a key driver of the interest in the business because the mineral is an important building block for low-carbon technologies such as solar farms and electric cars.