In the video in which Jenrick made the claim, he called for the UK to leave the European Convention on Human Rights (ECHR).
The ECHR is a treaty which sets out the rights and freedoms people are entitled to in countries that are signed up to it.
The treaty is overseen by the European Court of Human Rights in Strasbourg, France.
In the video, Jenrick said: “Our special forces are killing rather than capturing terrorists because our lawyers tell us that if they’re caught, the European court will set them free.”
In an interview on BBC Radio 4’s Today programme, Jenrick was asked what evidence he had to back up his claims.
He said: “The point I was making was one that our former defence secretary Ben Wallace has made, which is that our human rights apparatus including the ECHR is encroaching on the battlefield.
“And it is impacting the decisions that our generals and military decision-makers are taking as to what kind of action is required in these difficult situations.”
Pressed on whether he knew special forces were killing rather than capturing terrorists, Mr Jenrick said: “As Ben Wallace has said in that interview, decision makers are being asked to make decisions which they might not ordinarily make, for example to call in a drone strike and take lethal action in that way.”
He added: “Of course I’m not going to elaborate on particular cases because these things, these cases are not things that any minister can speak about.”
Former defence secretary Grant Shapps, who is also chair of Cleverly’s campaign, said he had seen “no evidence at all” in his time at the Ministry of Defence to back up Jenrick’s claim.
Speaking to BBC 5 Live, he added that Jenrick had been reflecting on a “broader concern” about the ECHR, but the issue was “not as black and white as he presented”.
However, former Tory MP Bob Seely, who is backing Kemi Badenoch to be party leader, defended Jenrick’s comments, saying they were “true”.
In a social media post, external Seely, who served in Iraq and Afghanistan, said the Ministry of Defence’s “fear” of human rights lawyers and the ECHR meant “it was easier to drop bombs than arrest anyone or bring them to justice”.