A security watchdog could investigate the killing of British militants by an RAF drone strike but will be blocked from any scrutiny of ongoing operations, David Cameron said.
The Prime Minister said he was happy to consider a probe by the parliamentary Intellgence and Security Committee (ISC) into last month's military operation to take out suspected terrorist Reyaad Khan in Syria.
But with the Government insisting it would not hesitate to take similar action against others on a reported "hit list" of Islamic State (IS) extremists, he sad he would not "contract out" responsibility for the UK's anti-terror policy.
The revelation of the unprecedented strike on August 21 in the Islamic State stronghold of Raqqah - which also killed Ruhul Amin - prompted calls for a full examination of the legal justification.
Critics said any military action ordered without the prior approval of Parliament should be subject to a system of checks, with some suggesting the ISC should play a role.
Responding to criticisms that a new ISC was still to be set up four months after the general election, the Prime Minister said a Commons motion had been tabled to do so and he hoped a new chairman would be in place within days.
Pressed by the SNP's Westminster leader, Angus Robertson, to refer the drone strike to the body of MPs and peers, he said he would be "very happy to discuss that with the new chair".
But he added: "The only proviso I would put on is that the Intelligence and Security Committee cannot be responsible for overseeing current operations.
"The responsibility for current operations must lie with the Government and the Government has to come to the House of Commons to explain that.
"I am not going to contract out our counter-terrorism policy to someone else. I take responsibility for it.
"But I think it is important, after these events have taken place, that the ISC is able to make these sort of investigations."
The roll of individuals who pose a direct threat to British citizens is said to be topped by the notorious "Jihadi John", who features in films of hostages being murdered.
Defence Secretary Michael Fallon insisted the Government would "not hesitate" to act again despite a backlash over the drone operation which killed militants Khan and Amin on August 21.