Elliott is now calling for an in-depth, open and timely independent review of the petroleum business - with full disclosure of the review results.
"We reject both claims", BHP said in a statement, adding it will review Elliott's revised proposal in full and formally respond as appropriate.
'We understood from the start that unification requires BHP to cut through certain complexity - and that Australians in particular feel passionate about BHP remaining rooted in Australia, ' Elliott's letter said.
Mackenzie has previously said it is the wrong time for BHP to sell its US petroleum assets, given oil prices are still relatively low at about $52 per barrel.
Chief Executive Andrew Mackenzie met Wednesday with representatives from Elliott Management Corp., the activist investor pushing for the resources company to shed at least some of its oil-and-gas assets and boost shareholder returns.
In fact Elliott Advisors has made a 180 degree change in its plans for shaking up BHP after being confronted by opposition from not only the Federal government but a string of local investors concerned that the original plan would damage the value of their shareholdings by cutting back on dividend imputation and other benefits from the company being based in Australia.
"If there is a natural owner out there who believes more upside can be achieved within this shale business than we do, then we will be more than happy to talk to them", he said.
A source close to BHP said the company expected to meet Elliott in Barcelona.
The fund manager today also took aim at BHP's use of a Singapore marketing subsidiary to try to reduce tax liabilities in Australia, commonly known as a Singapore tax sling.
"The current period of shareholder activism could result in a break-up and/or a significant adjustment of the company's structure", Citi said in a note this week.
However, BHP says the costs and associated risks of Elliott's proposal would "significantly outweigh any potential benefits". Instead of taking offence, BHP could accept Elliott's challenge, invite bidders for its oil business, and know that it is doing so from a position of strength.
BHP advanced 0.8 percent to A$24.02 in Sydney trading Tuesday, extending gains in the past year to 29 percent.
Such a buyback, if the current valuation remained unchanged, would lead to $2.4 billion in value accretion, equivalent to more than 12 times Elliott's expected costs of unifying BHP's dual listings, it said.