Jeremy Hunt has said it is not possible to "change or delay" the introduction of the controversial contract for junior doctors as it emerged that 500 medics have already signed up to it.
Doctors' leaders have said they will call off next week's strike if the Health Secretary removes his threat to impose the new contract.
The British Medical Association (BMA) said it was making a "clear offer" to Mr Hunt in a bid to avert the first all-out strike in the history of the NHS.
But in a letter to the BMA's junior doctor committee chairman, Dr Johann Malawana, Mr Hunt said: "It is not now possible to change or delay the introduction of this contract without creating unacceptable disruption for the NHS."
The strike is scheduled to start next Tuesday morning and will see thousands of junior doctors across England withdraw full labour - even emergency care.
The General Medical Council warned that some hospitals may "struggle to cope" during the strike.
In advice the regulator issued to all doctors in training, the GMC said that where hospitals were struggling "the right option may be not to take action that results in the withdrawal of services for patients".
The advice adds: "If, during the industrial action, it becomes clear that patients are at risk in a local area because of inadequate medical cover, and doctors in training are asked in good faith to return to work by employers, we expect they would fulfil this request.
"In the event of an emergency, we know doctors in training will always come forward. Where contingency plans are overwhelmed, it is vital that doctors taking action can be contacted and are available to help."
Earlier, Dr Malawana requested an urgent meeting with Mr Hunt and said the key to ending the strike lay in Mr Hunt's hands.
Dr Malawana added: "With preparations under way for the first full walk-out of doctors in this country, the Government cannot continue to stick its head in the sand.
"It must now listen to the many voices raising concerns about its mishandled plans and do what it has refused to for far too long: put patients first, get back around the table and end this dispute through talks."
In his letter to Dr Malawana, Mr Hunt wrote: "It is clear that the industrial action you plan will put patients in harm's way. The first step to averting this must be serious recognition of the offer that Sir David made, so that we can have talks about the many other areas where training and quality of life can be improved for junior doctors.
He added: "We must be clear that anyone deciding - at your urging - to withdraw potentially lifesaving care for patients is making a choice to do so. Many will find this disproportionate given the matter still in dispute is Saturday pay rates."
A Department of Health spokeswoman added: "We have today written to the BMA to make clear that it is not credible to call for imposition to be lifted when they refused to negotiate on the one remaining issue of Saturday pay that separates the two sides.
"More than 500 doctors have already signed up to a new contract that was 90% agreed with the BMA, following 75 meetings and 73 concessions made by the Government."
Junior doctors will fully withdraw labour between the hours of 8am and 5pm on April 26 and 27.
In previous strikes, junior doctors provided emergency care cover.
The major sticking point has been over weekend pay and whether Saturdays should attract extra "unsocial" payments.
Currently, 7pm to 7am Monday to Friday and the whole of Saturday and Sunday attracts a premium rate of pay for junior doctors. But the Government has said the Saturday day shift must be paid at a normal rate.