NHS leaders have said the strike action, which coincides with the Easter holiday, will be “challenging”.
Writing in The Times, the Prime Minister said patients would be left “paying the price”.
He said the offer was made after “months of collaboration with the BMA”.
Sir Keir wrote: “That is why walking away from this deal is the wrong decision. It is reckless. And doing so without even giving resident doctors the chance to vote on it makes it worse.
“Because the truth is this: no one benefits from rejecting this deal.”
He said resident doctors, the NHS and patients will be “worse off”, highlighting that each strike costs the health service £250 million.
“Progress slows. Waiting times fall more slowly. Pressure on staff increases,” he added.
“That is what makes this so frustrating — and so completely avoidable.
“So I say this to the BMA’s resident doctors’ committee: reconsider.
“Give members a say and put this deal to a vote.
“Failing to do so will mean resident doctors are left with less, the NHS is weakened, and patients pay the price.
“To resident doctors, I say this: make your voice heard. This deal improves your pay, your progression and your future. Do not let others decide for you.
“There are still 48 hours left to choose a better path. For patients, the NHS, and our doctors — I urge you to take it.”