The upcoming junior doctors' strike "risks the safety of many patients", the Health Secretary has claimed.
In response, the BMA rejected Mr Hunt's claims that the principal outstanding issue in the contract negotiation is Saturday pay.
They again offered to call off the strike if he agreed to lift the threat of imposing the contract while talks resumed.
On Saturday, Labour shadow health secretary Heidi Alexander urged Mr Hunt to test the contested new work contract in a small number of trusts rather than impose it across England without the support of the BMA.
However, the Health Secretary insisted that the Government was already planning to roll out the contract slowly and dismissed the proposal as Labour "opportunism".
Instead he wrote to the BMA chairman Mark Porter, saying: "Next week's withdrawal of emergency care by junior doctors, called by the BMA, seriously risks the safety of many patients who depend on the NHS."
The extreme action planned will be deeply worrying for patients and place enormous additional strain on our NHS at a time of intense pressure.
Mr Porter responded on Sunday, explaining the BMA's objections and calling on the Health Secretary to remove the threat of contract imposition as a settlement "cannot take place with the threat of imposition hanging over our junior doctors' heads".
He said: "For the sake of clarity, we must, once again, reject your assertion that the only outstanding issue in dispute relates to Saturday pay.
"Your own letter recognises a number of critical issues concerning work-life balance, excessive working hours, improvements in training and crucially, workforce and funding implications for seven day services.
"The proposed contract is deficient in failing to address these issues properly, hence our concerns for patient care, the long-term future of the NHS and the recruitment and retention of doctors."
The two-day all-out strike is set to start on Tuesday at 8am and the NHS has already cancelled 125,000 operations and appointments in preparation