A soldier from the Light Dragoons died while on a vehicle patrol, as part of Operation Panchai Palang, or Panther's Claw, in Lashkar Gah district, central Helmand Province.
In a separate incident, a soldier from 5th Regiment Royal Artillery was killed while on a foot patrol in Sangin district, Helmand Province. This was not part of the operation.
Next of kin have been informed
Lieutenant Colonel Nick Richardson, spokesman for Task Force Helmand, said: "These fine British soldiers made the ultimate sacrifice and their memory will live with us forever."
Meanwhile the Prime Minister insisted that Operation Panther's Claw had not been "in vain", despite the deaths of 20 British troops over the past month.
"The efforts of our troops in Helmand have been nothing short of heroic," Mr Brown told the Evening Standard. "There has been a tragic human cost. But this has not been in vain."
Mr Brown said it was now time to "commemorate" the British troops who have died in Afghanistan.
Twenty British personnel have been killed this month alone in Afghanistan - with 189 having died since the start of operations eight years ago.
During a constituency visit in Fife today, the Prime Minister said it has been "one of the most difficult summers" since troops went into Afghanistan.
He said: "Now that Operation Panther's Claw has shown that it can bring success and the first phase of that operation is over, it's time to commemorate all those soldiers who have given their lives and to thank all our British forces for the determination and professionalism and courage that they've shown.
"What we have actually done is make land secure for about 100,000 people.
"What we've done is push back the Taliban - and what we've done also is to start to break that chain of terror that links the mountains of Afghanistan and Pakistan to the streets of Britain.
"And I'm very proud of what our forces have achieved over the last few weeks - indeed for all the time they've been in Afghanistan."
He also echoed Foreign Secretary David Miliband's call earlier today for talks with more moderate Taliban elements.
Mr Brown said: "Our strategy has always been to complement the military action that we've got to take to clear the Taliban, to threaten al Qaida in its bases - while at the same time we put in more money to build the Afghan forces, the troops, the police.
"We build up the institutions in society in Afghanistan so there's strong local government.
"We help give people a stake in the future of Afghanistan and at the same time we try to bring over those elements that can now work with the democratic process.
"So, it's part of a strategy that involves Pakistan and Afghanistan as well.
"It's a civilian and military strategy and that's the way we will succeed in the long run - by letting the Afghan people take more control of their own affairs by building up their army and building up their police."
The first stage of the operation in the troubled southern province drew to a close as senior ministers urged the stepping up of efforts to engage moderate Taliban elements.
Foreign Secretary David Miliband said the insurgency was "divided", with many of those fighting against international forces doing so for "pragmatic" rather than ideological reasons.
International Development Secretary Douglas Alexander admitted there were concerns about holding talks while fierce combat was taking place.
"It is a difficult message for politicians to talk about the issues of reconciliation and reintegration when British troops are fighting the Taliban," he told the BBC Radio 4 Today programme.
"But I have confidence in the good judgment of the British people. I think people recognise from the experience of places like Northern Ireland that it is necessary to put military pressure on the Taliban while at the same time holding out the prospect that there can be a political process that can follow, whereby those that are willing to renunciate (sic) violence can follow a different path."
Downing Street stressed that the Government had not changed its position, and would only deal with Taliban elements who were willing to "renounce violence".
Mr Miliband said: "I think it is a very significant announcement; the extraordinary bravery and intelligence of our forces now means that some 80,000 Afghans are living within the orbit of legitimate governance and that is very significant indeed.
"The economic capital of Helmand Province is now joined to the provincial capital and it is vital that this sort of progress is followed up with the economic development and also the political strategy, which is going to be key to a sustainable settlement," he told BBC Radio 4's The World at One.
He added: "Our whole purpose in Afghanistan is not to create a new British colony, we are there to build sustainable Afghan capacity to defend themselves."
Mr Miliband stressed that what he termed "Afghanistan" or continuing to build up the political, economic and military structures in the country was now "absolutely key" to the mission.
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