A hand-written note at the bottom of the Prime Minister's letter to Mrs Fatima Khan says "You are in our thoughts and prayers".
The letter, dated December 20, calls Dr Khan's death a "sickening and appalling tragedy" and adds that "it is right that the Syrian regime should answer for it".
Dr Abbas Khan's sister, Sara, has told ITV News that she expects the British government to get answers from the Syrian regime. "This is the least they can do," she added.
The sister of the British surgeon Dr Abbas Khan who died in Syria said that the Prime Minister has sent the family letters.
Sara Khan told ITV News that David Cameron said "he is now going to help us get answers but nothing has actually been said as to how they expect to do this and when".
Scotland Yard is to be involved in the post-mortem process surrounding the death of British doctor Abbas Khan, the family's solicitor has said, after his body was flown back to the UK.
Nabeel Sheikh issued a statement which read:
The family of British surgeon Abbas Khan have employed an independent pathologist to oversee the post mortem on his body following his death in a Damascus prison.
Nabeen Sheik, a lawyer for the family said the results of the post mortem were expected tomorrow.
The body of Dr Khan was returned to the UK today.
The mother of a British surgeon has demanded answers after accusing Syria of "killing" her son following his death in a Damascus prison.
The circumstances in which Dr Khan, a 32-year-old orthopaedic surgeon from London, died while in detention in Syria remains in dispute.
Speaking after his body arrived back in the UK Fatima Khan said: "I don't know why they killed my son and I want to ask why. Why on the release date they killed my son, I want answers. They are liars, every ministry is liars in Damascus."
Chiltern Railways says it has been advised to operate its services between London and Birmingham at half speed tomorrow because of expected high winds.
Network Rail could put in emergency speed restrictions of 50mph in place during the stormy conditions, which are forecast to hit the Midlands tomorrow afternoon.
The train operator is warning passengers to expect severe disruption, and are allowing anyone with pre-booked tickets for Monday 23 December to travel on services today.
It follows a similar move by London Midland, East Midlands, Virgin and Cross Country services.
The body of a British doctor who died in custody in Syria has arrived back in the UK.
Dr Abbas Khan, 32, was on the verge of being released when his family were told of his death by what the Syrian government calls suicide and they say was political murder.
The orthopaedic surgeon from London was captured in November 2012 in the ancient city of Aleppo after travelling from Turkey to help victims of hospital bombings.
The International Committee of the Red Cross had earlier transported his body from Damascus to the Lebanese capital Beirut, where it was received by his mother Fatima Khan and British officials