BBC News reports that five months before the murder of soldier Lee Rigby in London, his killer Michael Adebowale said that he wanted to kill a soldier, during a 'graphic and emotive' Facebook discussion.
The Intelligence and Security Committee of Parliament (ISC) believes that Facebook doesn't have an obligation to identify such conversations.
A Facebook spokeswoman told the BBC: "Like everyone else, we were horrified by the vicious murder of Fusilier Lee Rigby.
"We don't comment on individual cases but Facebook's policies are clear, we do not allow terrorist content on the site and take steps to prevent people from using our service for these purposes."
The ISC does believe that the social network giant should do more however, and stated: "Had MI5 had access to this exchange, their investigation into Adebowale would have become a top priority.
"It is difficult to speculate on the outcome but there is a significant possibility that MI5 would then have been able to prevent the attack."
The public version of the ISC's report doesn't name Facebook as the service which hosted the conversation, although the BBC says it understand that it does do so in the uncensored version given to the Prime Minister.
The report says that there's a risk of Facebook becoming a "safe haven for terrorists to communicate within" due to its failure to make such conversations known to the authorities.
Companies such as Apple, Google, Microsoft, Twitter, Yahoo, and Facebook have said in the past that they have a duty to protect their members' privacy.
TechUK is a lobbying body that works with Facebook, and their chief executive Andy Walker said: "If the government believes that it needs additional powers to be able to access communication data it must be clear about exactly what those powers are and consult widely on them before putting proposals before Parliament."
A "substantial" online conversation was identified in December 2012 between Adebowale and a foreign-based extremist, who's referred to as Foxtrot. In it Foxtrot is reported to have talked of ways to kill a soldier, with the inclusion of a knife.
Foxtrot is said to have links to AQAP, a Yemen-based terror group, but this was not known to UK authorities at the time.
Following Lee Rigby's murder a third-party, who's unidentified, came through with a transcript of the conversation and gave it to GCHQ.
The information provided also included details on Adebowale's several accounts on the service - 11 in total. Seven of the accounts were disabled by Facebook, with at least five of them because of links to terrorism, two for reasons unrelated to terrorism. One was also disabled by Adebowale himself.
The accounts that were disabled by Facebook were via an automated process, so no actual individual looked at the content and reviewed it to possibly pass it on to the authorities.
The account which held the phrase "Let's kill a soldier" was not one of the accounts automatically close by Facebook's software.
The report ends with: "Companies should accept they have a responsibility to notify the relevant authorities when an automatic trigger indicating terrorism is activated and allow the authorities, whether US or UK, to take the next step.
"We further note that several of the companies attributed the lack of monitoring to the need to protect their users' privacy. However, where there is a possibility that a terrorist atrocity is being planned, that argument should not be allowed to prevail."
Jim Killock, executive director of the Open Rights Group responded to the report by saying: "The government should not use the appalling murder of Fusilier Rigby as an excuse to justify the further surveillance and monitoring of the entire UK population.
"The committee is particularly misleading when it implies that US companies do not co-operate, and it is quite extraordinary to demand that companies pro-actively monitor email content for suspicious material.
"Internet companies cannot and must not become an arm of the surveillance state."