Shares in BHP Billiton jumped by nearly 5% intraday on Monday after one of its major shareholders pressurised the FTSE 100 mining giant to adopt a restructuring plan.

Elliott Advisors, UK subsidiary of New York, US-based hedge fund Elliott Management Corporation founded by Paul Singer, said the miner should demerge its US oil business and return money to shareholders.

"The goal is to provide details of the BHP shareholder value unlock plan to all of BHP's shareholders, so that BHP can engage openly with all parties on the plan," Elliott, which holds 4.1% of BHP's Billiton's London-listed equity, said in a statement.

Outlining, a three-step plan, the hedge fund said the first step should entail unifying BHP's dual-listed company structure into a single Australian-headquartered and Australian tax resident listed company

"Second step should include demerging and separately listing BHP's US petroleum business on the New York Stock Exchange, and finally the third step would include adopting 'a consistent and value-optimised capital return policy'; an opportunity to monetize the substantial franking credit balance through discounted off-market buybacks," according to Elliott.

In response, BHP Billiton's shares rose by as much as 4.6% before surrendering some of the gains. At 1:46pm BST, the company's shares were up 3.1% or 38.50p to 1326p.

However, BHP said: "After reviewing the elements of Elliott's proposal, we have concluded that the costs and associated risks of Elliott's proposal would significantly outweigh any potential benefits."