But Reprieve, the legal rights charity who represents Aamer, told HuffPost UK that Cameron has far more power to secure the detainee's release than was revealed in the letter to his 15-year-old daughter Johina Aamer.
Aamer is on hunger strike, along with 104 other inmates in Guantanamo, having been cleared for transfer out of the detention camp, but not for release.
The Guantanamo detainee, who is a Saudi citizen, was accused of leading a fighting unit for Al Qaeda in Afghanistan in 2001.
Aamer, who is also suspected of communication with shoe bomber Richard Reid, has a British wife and four children who all live in South London. He has been detained for 11 years.
His defence claims all evidence against Aamer came from unreliable witnesses or was gained under torture.
In April, a petition to free Shaker Aamer, started by Johina, gained 100,000 signatures, enough to secure a debate on the issue in the House of Commons.
Cameron told her: “Despite efforts to secure his release, it remains the case that he has been cleared for transfer but not for release.
"It also remains the case that any decision regarding your father’s release remains ultimately in the hands of the US Government.”
Clive Stafford Smith, director of Reprieve and Shaker's lawyer, said: "It is the repeatedly stated policy of the UK government that Shaker can and should come home to the UK.
"This is in David Cameron's hands and to suggest that he doesn't have the power to influence the US in this matter is slightly embarrassing."
The Prime Minister said in his letter the issue had been repeatedly raised with the US, including reports of Aamer's hunger strike. “The US authorities have assured us that he is in a stable condition and that he is being offered medical treatment," he added.
Johina told the Times: “My family and I are grateful to the Prime Minister for having the courtesy to respond to us directly after being ignored by the Labour Government. However, 11 years is too much for anyone to take, and our desire is that the UK uses ... its political strength to force the US to return our father home to us.”Suggest a correction