The Cordoba Foundation, which works for peaceful relations between Muslims and the west, invited Dr Abdul Wahid, chair of Hizb ut-Tahrir, to speak at a debate in February as part of a council-funded project.
Tony Blair briefly considered banning Hizb ut-Tahrir in the wake of the terrorist attacks in London on 7 July 2005 because he feared that the organisation glorified terrorism.
The foundation won £38,000 from the council as part of the Government's Preventing Violent Extremism Pathfinder Fund to deliver a Muslim media project and debating society.
But the council deducted £4,000 from that grant on the grounds that this was the cost of organising the February debate.
A spokesman for Tower Hamlets Council confirmed that it would provide no further funding to the foundation after it refused to withdraw its debate invitation to Wahid.
"It was felt that the partnership principle underpinning the joint work between the council and the Cordoba Foundation had broken down," the spokesman said. He added that the decision was by mutual agreement.
Third Sector was unable to contact the Cordoba Foundation.