One of its suicide bombers blew up Gandhi as he prepared to speak at a rally. The LTTE, decimated in May, denied killing Gandhi.
The sources said Sonia Gandhi was keen to expose the conspirators behind the murder of her husband even after LTTE chief Velupillai Prabhakaran and his intelligence chief Pottu Amman were killed by the Sri Lankan Army.
Prabhakaran and Pottu Amman, the Gandhi killing masterminds, were wanted in India for the assassination.
The MDMA's extension comes after a three-month delay after its term expired May 31.
The MDMA, now running on a skeleton staff, was set up on the recommendation of retired judge Milap Chand Jain, whose own inquiry into the conspiracy theory was called off in 1998.
Jain wanted the MDMA to look into several areas he could not investigate.