Khadr is accused of killing a US soldier with a grenade in Afghanistan in 2002 and has been held for seven years.
The 21 cases include the trials of five people accused of plotting the September 11, 2001, attacks on the US.
Prior to his inauguration, Obama said he would close down the Guantanamo Bay detention centre.
Jamil Dakwar, the director of the human rights programme at the American Civil Liberties Union, said Obama's request was a positive step but "the president's order leaves open the option of this discredited system remaining in existence".
Prosecution lawyers had been seeking to halt the military tribunals pending a review by the new US administration, with the option of them being restarted at a later date.
|Human rights groups have condemned the
treatment of Guantanamo prisoners [EPA]
But defence lawyers have called for the charges to be withdrawn in a way that would allow them to be re-filed under a different legal system.
The legal manoeuvrings came after a military judge adjourned the Guantanamo Bay military court ahead of Obama's swearing-in as US president.
Prior to his inauguration, Obama had vowed to close down the detention centre, which was set up by George Bush, the former US president.
About 245 people are still held at the prison camp in Cuba.
The Bush administration had said it planned to put 80 prisoners on trial facing war crimes charges, but only three cases have been completed.