"We have created space in which we can have Afghan government, Afghan police and Afghan forces and that will make it very difficult for the Taliban and Al Qaeda to reassert themselves," he said.
"Three quarters of the terrorist plots that hit Britain derive from the mountain areas of Pakistan and Afghanistan," he said.
"And it is to make Britain safe and the rest of the world safe that we must make sure we honour our commitment to maintain and keep a stable Afghanistan."
Mr Brown insisted "every effort" was being made to ensure troops had the best security and equipment.
"We have increased dramatically the resources we are spending in Afghanistan to deal with this new kind of threat which is the roadside bomb, the electronic devices, the guerrilla warfare."
By Ian Pannell, BBC correspondent in Kabul
"Every year the level of violence has increased and with it the casualty rate.
There are now growing criticisms about whether enough progress is being made, whether the strategy is right and whether or not British troops are protected enough in a conflict that still shows no signs of easing.
The latest deaths come just four days before presidential elections. UK troops have been trying to make areas safe ahead of voting but that means more fighting and even more deaths as the insurgents try to disrupt the poll."
The Royal Welsh soldier had been on vehicle patrol near Musa Qala in Helmand province on Thursday morning when he was hit by the explosion.
He died at a military hospital in Selly Oak, Birmingham, on Saturday. Neither he nor the Royal Regiment of Fusiliers soldier has been named, but their next of kin have been informed.
A total of 10 UK personnel have died this month as troops attempt to shore up security ahead of August elections.
The latest deaths follow those of three soldiers killed by roadside bombs while on foot patrol in Helmand on Thursday.
Two had been attempting to help a comrade who had been wounded by an earlier blast.
Rifleman Daniel Wild, 19, from Easington in County Durham, and Captain Mark Hale, both serving with the 2nd Battalion The Rifles, were carrying Lance Bombardier Matthew Hatton, 23, of 40 Regiment Royal Artillery, from North Yorkshire, when they were hit by a second explosion.
Their patrol had been part of an operation intended to provide security for a pre-election Shura, or meeting of elders.
Colonel Richard Kemp was the commander of the British Army in Afghanistan when it went into Helmand.
He said: "The Taliban have learnt a very hard lesson for themselves. They can't take us on head to head and toe to toe and have resorted more to this kind of device.
"Although our death toll is bad, theirs is considerably worse and sometimes we are talking about a ratio of 100 to 1 against the Taliban."
Defence secretary Bob Ainsworth said news of the latest deaths made it a "grim day" and said Britain mourned every loss of life in the conflict.
Gordon Brown: "We must never forget why we are in Afghanistan''
But he insisted UK troops had been making "good progress" in their mission.
He accepted the recent offensive against the Taliban - Operation Panther's Claw - was a "tough fight", but said it had brought nearly 80,000 Afghans out from under the "tyranny of the Taliban".
Mr Ainsworth also said he believed the second Afghan presidential elections, to be held later this week, would offer more Afghans "a stake in their own emerging democracy" and provide greater security for the UK.
"It is only by supporting the Afghan government and its security forces to bring stability can we ensure that we prevent Afghanistan becoming the haven for terrorists it once was, protecting Britain from attack and promoting peace across the region.
"We must not fail in this task, and we will not."
Shadow defence secretary Liam Fox said passing the 200th death mark served as a "stark reminder of the bravery and sacrifice of British troops in Helmand".
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