The newspaper quoted Cameron's spokesman as saying that Cameron "highly understands the pain of Fusilier Rigby's family", and that "any meetings that they [the family] ask for they will get."
In an interview with The Telegraph, Rigby's family said that they want answers from Cameron.
"He is the only one that has the full report," Phil McClure, the soldier's father, told the Telegraph.
Meanwhile, Sara McClure, Lee Rigby's sister has accused Facebook of having her brother's "blood on their hands," as quoted by the newspaper.
Lee Rigby, a soldier in the British army, was hacked to death in broad daylight in southeastern London on May 22, 2013 by Michael Adebowale and Michael Adebolajo. They were sentenced to a minimum of 45 years and life imprisonment respectively.
On Tuesday, the ISC published a 200-page report, according to which the murder of Lee Rigby could not have been prevented by MI5, since an Internet company had not shared an important piece of Adebowale's online exchange with an extremist abroad.
Several major British media sources have named Facebook as the company that had failed to pass on the vital information to intelligence services. However, the ISC report did not specify, via which exact online platform Adebowale discussed the plot to murder a soldier.