In an interview with the British Forces Broadcasting Service, Brown paid tribute to the 'sacrifice' of the soldiers who had died.
"I know that this has been a difficult summer - it is going to be a difficult summer. These sacrifices that have hurt so many families in our country are ones that the whole of Britain will want to acknowledge. I think the operation we are engaged with is showing signs of success. Our troops are making progress as they attempt to make the area safe," Brown said.
Brown's comments came after parents of some soldiers killed in Afghanistan accused the Government of starving British forces of urgently needed equipment.
Brown said commanders had assured him in a lengthy briefing that the Operation Panther's Claw offensive to drive the Taliban from central Helmand province was making "considerable progress".
"This is a patriotic duty. Of course people want to know if the action we are taking is the right action. It comes back to terrorism on the streets of Britain. If we were to allow the Taliban to be back in power in Afghanistan and al-Qaeda then to have the freedom of manoeuvre it had before 2001, then we would be less safe as a country," Brown said.