Anglo American has rebuffed a third takeover attempt by BHP after the Australian company sweetened its offer in an attempt to create a global mining titan.

BHP said it had submitted an “increased and final” bid of £31.11 a share for Anglo, which values the FTSE 100 company at £38.6bn, earlier this week.

Anglo had already rejected two previous offers from BHP: the first, in April, valued it at £31bn and the second, which was snubbed last week, put it at £34bn.

The attempted BHP takeover, the largest ever in the mining sector, would create a global player in markets for commodities including copper, iron ore, potash and metallurgical coal used for steelmaking.

Copper in particular is in high demand as a raw material in the transition to low-carbon energy as it is used in manufacturing components for electric vehicles and renewable energy projects. Anglo’s key assets are copper mines in Chile and Peru.

After the two previous rejections, BHP said it had been “engaging with Anglo American and its advisers” to allay concerns over the deal and that it was hopeful that resolution would be reached in the next seven days.

Mike Henry, the chief executive of BHP, said: “The revised proposal is underpinned by BHP’s disciplined approach to mergers and acquisition and our focus on delivering long term fundamental value.

“BHP’s revised proposal will offer immediate value for Anglo American shareholders and allow them to benefit from the long-term value generation of the combined group.”

BHP’s attempt to snap up Anglo could still be gatecrashed by a rival. The Swiss mining company Glencore has reportedly been considering its own approach.

BHP’s terms require that Anglo sells its stakes in Anglo American Platinum and Kumba Iron Ore, returning cash to shareholders as part of the deal.

Even if BHP is unsuccessful, Anglo’s chief executive, Duncan Wanblad, has pledged to break up the business and sell its platinum division and its De Beers diamond arm.

Stuart Chambers, the chair of Anglo American, said: “The board considered BHP’s latest proposal carefully, concluded it does not meet expectations of value delivered to Anglo American’s shareholders, and has unanimously rejected it.”

Chambers said its board was “confident in Anglo American’s standalone future prospects” and that BHP had not addressed the board’s concerns about the complex terms of the takeover.

“Multiple engagements with the BHP team have not yet been able to resolve the concerns on these issues,” he said.

Anglo received a boost this week when one of its largest shareholders, Legal & General Investment Management, backed the FTSE 100 miner’s break-up plan, calling it a “radical but attractive strategy”.

The South African government is Anglo’s largest shareholder through its Public Investment Corporation (PIC) and home to many of its mines. The PIC has so far been unimpressed by BHP’s takeover attempts and said on Wednesday before the latest bid was made that the previous offer needed “meaningful revision”.

BHP had until 5pm on Wednesday to make an improved offer or walk away for six months under City takeover rules. Anglo said the deadline has now been extended until 29 May.