Turkey’s ambassador to Britain and the chief executive of the country’s national airline have been called to appear before MPs following the disappearance of three teenage girls who are believed to have flown to Istanbul before heading to Syria to join Islamic State (Isis).

David Cameron has indicated that security arrangements at the border and on aeroplanes could be tightened to prevent young people travelling to join the extremist group and has asked the home secretary, Theresa May, and the transport secretary, Patrick McLoughlin, to examine “all the protocols we have in place”.

Commons home affairs select committee has called Turkish Airlines chief executive, Temel Kotil, and the Turkish ambassador, Abdurrahman Bilgic, to give evidence about the problem of youngsters using Turkey as a route to Syria’s battlefields.

Shamima Begum, 15, Kadiza Sultana, 16, and 15-year-old Amira Abase are currently being searched for after they boarded a Turkish Airlines flight from Gatwick airport to Istanbul last Tuesday.

It is believed they have travelled into Syria to join the radical militant group.

The home affairs select committee chairman, Keith Vaz, said the Turkish witnesses had been called to appear before the cross-party group on 10 March, along with the Metropolitan police commissioner, Sir Bernard Hogan-Howe.

Vaz said: “It is shocking that at least four girls have flown unaccompanied using Turkish Airlines as part of their journey to reach Isis without the British authorities being alerted.

“Without taking serious and urgent action on an international scale, more and more brainwashed young people are likely to follow in these girls’ footsteps.

“The committee would like to hear from both the chief executive of Turkish Airlines and the Turkish ambassador to get their views on potential means of tackling this growing problem, of improving our collaboration on an international level, and on what we can do to help.”

During Wednesday’s prime minister’s questions, Cameron said: “What I have done is ask the home secretary to look urgently with the transport secretary at all the protocols we have in place about young people and travelling and what airlines do and what we can do.”

He denied a claim by Turkey’s deputy prime minister, Bulent Arinc, that there was a delay in informing the authorities in Istanbul about the girls.

“My understanding is that the police did respond relatively quickly in terms of informing the Turkish authorities and what the Turkish deputy prime minister has said about a three-day delay is not accurate,” he said.

“But there are always lessons to learn on this occasion. I suspect the lessons will not just be that we can tighten arrangements on aeroplanes and at our borders but also we all have a responsibility – schools, parents, families, communities, universities, colleges all have a responsibility to fight this poisonous radicalisation of young people’s minds.”

The education secretary, Nicky Morgan, has written to Bethnal Green Academy, the school attended by the three teenage girls, offering her support and saying she knows staff are doing everything possible to keep pupils safe.

In a letter addressed to Mark Keary, principal of the east London school, Morgan said that while everyone was hoping and praying for the schoolgirls’ safe return, thoughts were also with their friends and classmates who will “no doubt struggle” to come to terms with recent events.

Morgan’s one-page letter, published by the Department for Education, said: “I am writing to thank you and your staff for everything that has been done over the weekend to provide reassurance to parents and pupils on their return to the school yesterday.

“I know this must be a difficult time for everyone involved with Bethnal Green Academy, but I understand from my conversations with the regional schools commissioner, Tim Coulson, that your communications with parents and pupils have been clear and effective, and that you feel confident that everything possible is being done to keep pupils safe.

“While we hope and pray for the safe return of the pupils in question, we also think of their friends and acquaintances at the school who will no doubt struggle to come to terms with the events of recent days.

The letter continued: “I know that you and the staff there are doing everything possible to provide them with the help and support they need and to ensure they continue to thrive in a safe, tolerant environment where the fundamental British values of democracy, the rule of law, individual liberty, mutual respect and tolerance are promoted and widely shared.

“I have asked my officials to ensure that you and your staff continue to receive all the support and assistance that you require. If there is more that the RSC and others at the DfE can do to support you, please do not hesitate to get in touch.”

Last night, Scotland Yard said counter-terrorism officers leading the investigation “now have reason to believe that they are no longer in Turkey and have crossed into Syria”.

A spokesman added: “Officers continue to work closely with the Turkish authorities on this investigation.”

Keary said on Tuesday that he was shocked and saddened by the girls’ disappearance, but added that police had not found evidence they were radicalised at school.

He said police spoke to the girls after another student disappeared in December and indicated at the time that there was no evidence they were at risk of being radicalised or absconding. Access to social media at the school was strictly regulated, he added.

A tweet sent from an account under Shamima’s name was sent to Aqsa Mahmood, who left Glasgow for Syria to be a “jihadi bride” in 2013.

Relatives of the three schoolgirls have made emotional pleas for them to come home amid fears they may have been recruited by jihadists on the internet.