Home Secretary Theresa May has laid flowers at the scene of the attack.
A total of 38 people were killed on a beach near Sousse by a gunman with links to Islamic State extremists.
All Britons injured in the attack will be returned to the UK within 24 hours, Downing Street said.
An RAF C17 transport plane left Brize Norton in Oxfordshire on Monday at lunchtime bound for Tunisia to help evacuate casualties.
The prime minister said that if families wished, aircraft could help return their loved ones’ bodies to the UK.
He told BBC Radio 4’s Today programme the “absolutely horrific” events had “shocked the whole of the world”.
He said IS posed “an existential threat” to the West, and its members in Iraq and Syria were plotting “terrible attacks” on British soil.
Mr Cameron – who chaired another meeting of the Cobra emergency committee on Monday morning – said the UK must have a “full-spectrum response” to the IS threat – including continuing with air strikes.
https://www.endtime.com/wp-content/uploads/2017/06/83911583_ba2d36d4-f002-4542-b2b3-4951bc288432.jpg 371 660 alphatimes https://endtime.com/wp-content/uploads/2020/06/endtime-logo.png alphatimes2015-06-29 00:00:002018-03-28 16:09:24Tunisia attack: Cameron says IS fight ‘struggle of our generation’