The committee heard that Syria has become a haven for jihadists since the outbreak of the civil war, and hundreds of British citizens have travelled to the country as a result.
MI5 chief Andrew Parker said there are thousands of people living in Britain today who support al Qaida, and the head of MI6 Sir John Sawers warned the threat of terrorist attacks against Britain is increasing.
Asked how concerned he was about terrorist tourism, Mr Parker told the committee: "It has grown recently and is growing at the moment, because of Syria.
"Syria has become a very attractive place for people to go for that reason - those who support or sympathise with the al Qaida ideological message.
"We've seen low hundreds of people from this country go to Syria for periods and come back - some large numbers are still there - and get involved in fighting.
"This is partly because of the proximity of Syria and the ease of travel there, but also because it is attractive as what they would see as a jihadi cause."
Mr Parker said: "It is a very important strand of the threat we face, the way in which there is interaction between people who live in this country who sympathise with or support the al Qaida ideology and then travel to areas where they meet these al Qaida groupings, either al Qaida itself in south Asia or some of these other groupings across other regions.
"The attractiveness to these groupings is that they meet British citizens who are willing to engage in terrorism and they task them to do so back at home, where they have higher impact, in this country.
"We've seen that played out in previous plots here, including 7/7."
The case of Edward Snowden has been very damaging. Our adversaries were rubbing their hands together with glee and al Qaida were lapping it up.
Sir John Sawers was extremely critical of the leaks and the subsequent publication of the documents across the world.
Sir John said: "The case of Edward Snowden has been very damaging. Our adversaries were rubbing their hands together with glee and al Qaida were lapping it up."
GCHQ chief Sir Iain Lobban said he could give the committee specific instances of terrorists adapting their methods of communication because of the leaks.
Quizzing Sir Iain, ISC chair Sir Malcolm Rifkind said many believe the "real cyber threat" comes from GCHQ seeking to collect data communications.
Sir Iain replied: "We do not spend our time listening to the telephone calls or reading the e-mails of the majority, the vast majority that would not be proportionate, it would not be legal. We do not do it.
"It would be very nice if terrorists or serious criminals used a particular method of communication and everybody else used something else. That is not the case.
"It would be very nice if we knew who the terrorists or serious criminals were but the internet is a great way to anonymise and avoid identification. So we have to do detective work."
Sir Iain said the internet was an "enormous hayfield" and GCHQ was trying to access "those parts of the field that we can get access to and which might be lucrative in terms of containing the needles or the fragments of the needles we might be interested in, that might help our mission".
He went on: "We can only look at the content of communications where there are very specific legal thresholds and requirements which have been met. So that's the reality. We don't want to delve into innocent emails and phonecalls."
Sir Iain said: "I feel I have to say this - I don't employ the type of people who would do. My people are motivated by saving the lives of British forces on the battlefield. They're motivated by finding terrorists and serious criminals."
"If they were asked to snoop I wouldn't have the workforce, they'd leave the building," he added.
Both Mr Parker and Sir John insisted that the security agencies would not pursue any leads against potential terrorist plots which would involve the torture or mistreatment of suspects.
Sir John said: "There are very strong ethical standards in all our services.
"When you are working in a secret organisation, having a very strong ethical and disciplined approach is really, really important. That's one of the bases on which we recruit people."
Asked by Labour MP Hazel Blears if he could say the agencies were "beyond reproach" on this issue, he said: "I'm very confident to be able to answer your question 'Yes'."
Challenged over how the agencies would respond if they believed a suspect being held abroad had information which could prevent an attack in Britain, Sir John said: "We would do everything we can within the law to disrupt any such threat .
"If this person is held in a country where we've got a partnership relationship, we would seek with that partner to ensure that the right questions are put to that person, but in a lawful way.
"If there is a serious risk that our questions would prompt the maltreatment or torture of a detainee, we would consult ministers about that. If we knew that that was going to happen we wouldn't even think about it in the first place, we wouldn't even bother ministers with it."
Mr Parker added: "Would we pursue a situation that we knew would lead to mistreatment or torture of an individual to get terrorist threat intelligence? The answer is absolutely not.
"We do not participate in, incite, encourage or condone mistreatment or torture, and that is absolute."
Sir John said agents did not act like fictional spy James Bond, and disappear into the field for months on end with out contacting their superiors.
The committee also heard that only a "small number of people" are behind the terror threat in Northern Ireland, and Mr Parker described them as a "residue from a by-gone era."
He said: "Over time it's diminishing year on year and eventually we will see a Northern Ireland without this sort of terrorism."