The Free Babar Ahmad campaign has collected more than 12,000 signatures for an e-petition, a spokesman said.
It hopes to get more than 100,000 signatures by 10 November in a bid to get the coalition government to respond to its demand of putting Ahmad on trial in the UK. Ahmad has spent seven years in British high-security prisons without trial as he fights extradition to the US on terror charges.
The American authorities accuse the computer expert of running websites that urged Muslims to wage holy war and conspiring to raise funds for al-Qaeda and the Taleban in Afghanistan.
He denies the allegations and insists he is simply a peace-loving man dedicated to his family and his local community in Tooting, south London.
Ahmad’s father Ashfaq said: “As a result of the UK’s extradition laws, Babar has been imprisoned without trial since the 5 August, 2004.
“Over 12,000 people have recently signed the e-petition for him to be tried in the UK.
“All of these people believe that our extradition laws should be amended to prevent bundling my son, Gary McKinnon (the alleged internet hacker] and others like them on to a plane to America.
“The government has undertaken its extradition review – the time for action is now.”
Mr Ahmad was first arrested by Metropolitan Police officers in a dawn raid on his home in December 2003 on suspicion of leading a group which provided al-Qaeda and other terror networks with computer, financial and logistical expertise.
It was alleged that policemen subjected him to physical, verbal and sexual assaults and mocked his religion during the arrest, making him fear he would die and leaving him battered and bruised. In March, 2009, the Met agreed to pay him £60,000 in damages