Anglo had granted the Australian mining giant a one-week extension until 4pm on Wednesday, UK time (2am on Thursday AEST), to its original May 22 deadline to submit a binding offer after rejecting a third takeover proposal that it dismissed as difficult to execute.
BHP still has until then to make a firm offer or walk away.
BHP's shares closed flat on Wednesday at $A45.08.
Anglo's were down 0.7 per cent at Stg25.39.
London-listed Anglo agreed to hold talks with BHP to try to iron out concerns over the structure of the proposed deal, namely its condition that Anglo unbundle its South African platinum and iron ore units before the takeover.
In an earlier statement, BHP said it needed more time to engage with Anglo, while outlining commitments to minimise regulatory risk in South Africa.
Those commitments included job security for employees in South Africa.
BHP also said it would shoulder the costs of increased South African employee ownership that is expected to be required in any demerger.
"Throughout the engagements with BHP, BHP continues to restate its belief that the risks of its complex structure are not material, yet has repeatedly and consistently stated both publicly and during the engagements that it is unwilling to amend its proposed structure to assume these risks," Anglo said in its statement.
Anglo was founded in Johannesburg in 1917 and employs more than 40,000 South Africans, so any withdrawal would be a further economic blow to the country whose miners have been cutting jobs and investment as platinum especially falls out of favour.
South Africans are voting in an election on Wednesday, with polls suggesting the African National Congress could lose its majority after 30 years in power, in part due to anger about high unemployment and a stagnant economy.
JP Morgan analysts have estimated a takeover of Anglo by BHP could lead to outflows of $US4.3 billion from South Africa and weaken the rand.
BHP CEO Mike Henry has stood firm on the structure and value of its latest takeover proposal, focusing instead on allaying concerns around execution risk.
That risk includes Black empowerment provisions in South Africa that include local ownership stakes and assurances around employment security for workers in a nation with a jobless rate of more than 30 per cent, making it a key election issue.
There was also contention around whether there are sufficient buyers for Anglo's 69.7 per cent stake in Kumba Iron Ore and 78.6 per cent stake in platinum miner Amplats, said an investor who declined to be identified as the subject was sensitive.
