Anglo has rejected three proposals from BHP but last week agreed to a one-week extension to a deadline from Britain's takeover watchdog for BHP to make a formal offer or walk away.
In a statement to Australia's securities exchange, BHP said it was ready to offer a break fee to Anglo if the deal was blocked due to antitrust reasons or failed to get regulatory approval, saying it was sure it had quantified and managed such risk.
It also announced steps aimed at addressing concerns over its condition that Anglo divest some South African assets before a takeover can go ahead - one of the main sticking points in the talks.
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 $US4.3 billion ($A6.5 billion) from South Africa and weaken the rand.
BHP told the ASX on Wednesday it would make socioeconomic commitments to South Africa that include sharing costs related to increased employee ownership of Anglo's assets there, as well as maintaining employment levels at Anglo's Johannesburg office.
Anglo last week gave BHP a seven-day extension until Wednesday to its original May 22 deadline to submit a binding offer after rejecting a third takeover proposal it deemed too difficult to execute.
Anglo had no immediate comment when contacted by Reuters.
If Anglo does not agree to an extension, BHP will have to walk away or wait six months to make another approach - unless a rival bidder emerges - once the deadline expires.
BHP's shares closed flat on Wednesday at $A45.08 a share.
Anglo's were down 1.4 per cent at Stg25.23 pounds on Wednesday morning.
BHP's last-minute request comes after the miner had struggled to find common ground with Anglo by Tuesday, five sources told Reuters, with no new concessions granted on structure or value.
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 over 30%, 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.
