Jawad, who arrived at Guantanamo as a teenager, has been held at the US prison in Cuba for almost seven years, after being arrested in Afghanistan for allegedly injuring two US soldiers and their interpreter in a grenade attack.
"They came to the same conclusion that everyone else came to, that he's innocent," Major David Frakt, one of Jawad's military lawyers, told the Reuters news agency.
"I'm very pleased that the Obama administration is finally starting to restore the rule of law to detention operations."
The government's request to eventually release Jawad is in contrast to a statement last Friday by the US justice department.
It said it wanted to hold Jawad at Guantanamo while conducting a criminal investigation, saying it had new evidence from a witness.
Afghan return
In the newest court filing, prosecutors suggested that they could send Jawad to another country, avoiding the prospect of bringing him to the US to face trial.
Lawyers for Jawad have called repeatedly for the detainee to be sent back to Afghanistan, which has offered to send an aircraft to Cuba to pick him up.
"The Afghan government has told us that they believe he has suffered enough and they don't have any plans to prosecute him," Frakt said.
A federal judge could compel prosecutors to make a decision before the end of the three-week schedule for Jawad's release.
In a separate court action on Wednesday, a US judge ordered the release of another detainee held at the prison, Khaled Al-Mutairi from Kuwait.
Al-Mutairi was arrested in Pakistan in 2001 after travelling to Afghanistan with a charitable organisation to build mosques and provide funds for schools and orphanages.
The US justice department said it would review the ruling before deciding whether to appeal.
There are currently 229 detainees at the prison in Cuba, which Obama has pledged to close by January 2010.