Babar Ahmad, of Tooting, London, has been held in jail for seven years without trial while challenging extradition to the US.
His case will come up in a Westminster Hall debate on extradition later.
Mr Ahmad’s supporters say signatories are being dismissed by the failure to hold the debate in the Commons.
Under the e-petition system, an issue can be considered for possible debate in the Commons if it gathers more than 100,000 signatures.
Babar Ahmad, whose e-petition is one of only six to gain more than 100,000 supporters, has been held without trial for seven years in high-security conditions while he challenges his extradition at the European Court of Human Rights.
US prosecutors allege he was a global fundraiser for extremists in Afghanistan and Chechnya, through a website operated from south London but technically based in the US.
He is also accused of having obtained information about US Navy ships and their movements in the Gulf. He denies the allegations and his campaign team says he should be tried in the UK because this is where the alleged offences occurred. He has never been charged with an offence in the UK.
UK courts approved the extradition and the case is now at Strasbourg
Mr Ahmad’s family has asked the Director of Public Prosecutions to review the case. On Wednesday the Crown Prosecution Service confirmed that the DPP had received a file from Mr Ahmad’s lawyers setting out their case for a prosecution in the UK.
Shadow justice secretary Sadiq Khan, Mr Ahmad’s constituency MP and a supporter of the campaign, is expected to attend the session on Thursday, but Parliamentary convention prevents frontbenchers speaking during a backbench debate.
Green MP Caroline Lucas said she would be urging a full debate in the Commons.
She said: “That the e-petition to grant Babar Ahmad a UK trial has gained such astounding support so quickly shows the level of public anger.
“While I accept it is difficult for the backbench committee to devote parliamentary time in the Commons chamber to every petition that passes the 100,000 threshold, the fact that this campaign was not a high profile newspaper-led effort, but a purely grass roots one makes it a particularly strong contender.”
Earlier in the week, 100 lawyers, including seven QCs, wrote to Commons leader Sir George Young attacking the decision to relegate Mr Ahmad’s case to a debate in Westminster Hall, rather than allowing a vote in the Commons.
“The petition is one which goes to the heart of the values which we cherish so dearly – the right to a fair trial,” said the letter.
It said it was wrong to shunt Mr Ahmad’s case into Westminster Hall when the e-petition on immigration, with fewer signatures, is expected to be held in the Commons in the New Year.
Sir George told the BBC that the decision to hold the debate in Westminster Hall had been taken by the Backbench Business Committee, not the government.