Supporters from Free Babar Ahmad have collected more than 12,000 signatures for an e-petition, a campaign spokesman said.
They hope to get over 100,000 signatures by November 10 in a bid to get the Government to respond to their demand of putting Mr Ahmed on trial in the UK.
Mr Ahmed 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 fight holy war and conspiring to raise funds for al Qaida and the Taliban in Afghanistan. But he strenuously denies the allegations and insists he is simply a peace-loving man dedicated to his family and his local community in Tooting, south London.
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 Qaida 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 all over his body.
In March 2009 the Met agreed to pay him £60,000 in damages after he brought a personal injury case at the High Court but the four officers accused of beating him up were acquitted after a month-long trial at London’s Southwark Crown Court.
British-born Mr Ahmad was released six days after his arrest and has never been charged in the UK. But the Imperial College London IT administrator was again held by Scotland Yard officers in August 2004 on an international arrest warrant issued by American federal authorities.
The European Court of Human Rights halted extradition proceedings last July but a judge ruled he must remain in custody until a final decision is made later this year.