United States -- but who nonetheless are still in the world's most notorious prison. Some have been and continue to be beaten and mistreated by their jailers," the lawyers said in a letter released on Thursday.
"Mr President, our clients recognize the challenges you face. But we respectfully submit that finding a home now for 20 innocent men is a drop in an ocean.
"The continued imprisonment of these men makes us no safer and it shames America," they added, citing Obama's inauguration speech last month during which he said that "our security emanates from the justness of our cause."
Among the 20 detainees, whom the lawyers said "some have been and continue to be beaten and mistreated by their jailers," were 17 Chinese Uighurs, most of whom were cleared by the administration of George W Bush in 2003.
The United States has tried unsuccessfully for several years to arrange the transfer of the Muslim Uighurs to a third country, as Washington fears they could face persecution if they return to China.
Two of the 20 detainees are Algerians arrested in Bosnia in the late 2001 on allegations of planning an attack on the US embassy in Sarajevo. A federal judge called for their immediate release on November 20. One of them is Lakhdar Boumediene, who has been on hunger strike since December 2005.
According to his lawyer, Steve Oleskey, Boumediene "for ten days was taken to an isolated cell and forced to sleep and pray on a mat reeking from excrement" starting in late January, and was force-fed a protein-rich liquid through a tube inserted in one of his nostrils.
Mohammed al-Gharani, a Chadian who grew up in Saudi Arabia and has been held at Guantanamo for seven years after being arrested at the age of 14, remains in isolated confinement, his lawyer Cori Crider said, despite having been cleared by a federal judge on January 15.
The lawyers "urgently" requested that Obama "have all innocent men moved" to less restrictive cells, "treated humanely, respectfully and in accordance with the law," that allegations of mistreatment "be promptly and thoroughly investigated" and that Obama "immediately restore liberty to these men."
A minority of European Union countries -- France, Italy, Portugal and Spain -- have said they might be ready to accept former prisoners under strict conditions in support of Obama's decision to close the controversial detention site at the US naval base at Guantanamo.
But the widely differing laws among the 27 EU countries have made them struggle to define a common position on hosting the detainees.
A high-level EU delegation is to travel to Washington on March 16-17 to find out how US authorities decided that around 60 of the more than 240 remaining prisoners could be released and why they cannot be hosted by the United States.