When Malala returns to Pakistan, he said, "we will provide her with complete security, despite anyone's refusal, to ensure that something like this never happens again. The attack on Malala was a mindset of people who don't want to see this country progress."
Rosser said he would not discuss any security precautions the hospital may be taking.
The Taliban have claimed responsibility for the shooting in the conservative Swat Valley but don't appear to have anticipated the level of condemnation it would provoke.
Thousands of people in Pakistan and elsewhere have attended rallies and vigils honoring her courage and praying for her recovery.
Malala initially gained international attention in 2009, writing a blog about her life as the Taliban gained a foothold in her home region of Swat, a Taliban redoubt in northwest Pakistan, near Afghanistan.