Some 4,000 British soldiers are involved in the operation
A UK soldier has been killed in a major offensive in Afghanistan, the Ministry of Defence has said.
The soldier, of 1st Battalion Grenadier Guards, was killed in an explosion in Nad Ali District in Helmand Province. His next of kin have been informed.
Some 4,000 British troops are involved in the Moshtarak offensive against the Taliban and have secured "key objectives", Army chiefs said.
The operation is the biggest Afghan mission since the 2001 invasion.
More than 15,000 US, UK and Afghan troops swept into the Helmand districts of Marjah and Nad Ali in a bid to secure government control.
Operation Moshtarak - which means "together" in the local Dari language - is being led by 4,000 US Marines, supported by 4,000 British troops, with Canadians, Danes and Estonians.
The soldier was killed by an explosion while in a vehicle patrol during the early stages of the operation.
The death was one of the first among coalition forces in the offensive. A spokesman for Nato's Isaf (International Security Assistance Force) force said a second coalition soldier was killed by small-arms fire.
Prime Minister Gordon Brown offered his condolences to relatives and friends of the dead soldier, who he said was "very brave, very courageous" and died "making the ultimate sacrifice for our country".
Mr Brown said he was "proud of the exceptional role that British forces have played" in the operation.
He added that senior military figures had informed him that "they believe that this is a successful first phase in which the successes of the British forces have been exceptional".
The prime minister said what had already been achieved was "significant" but "we have got to build on that in the next few weeks so that the Afghan population in this area feel a great deal safer".
Lieutenant Colonel David Wakefield, a spokesman for Task Force Helmand, said the dead serviceman, who has not been named, "made the ultimate sacrifice doing his duty as part of this operation to clear the insurgents away".
He went on to say that the soldier's "selfless commitment and courage will not be forgotten".
More than 1,200 British troops are currently involved on the ground.
A further 3,000 British troops are also available if needed. A Ministry Defence spokesman said these troops were "providing wider support" such as logistics and moving equipment.
British forces have focused on gaining control of targets in the Nad-e-Ali district.
Maj Gen Messenger, the chief of the defence staff's strategic communications officer, said the "key objectives" of the operation had been secured in the early hours of Saturday.
He explained that "low numbers" of insurgents had been killed during the attacks, but added that efforts by British troops in the Chah-e-Anjir Triangle had been successful.
However, he stressed that there was "no complacency", since it was widely understood that "this is the easy bit".
He said: "The hard bit is what comes next in reassuring the public. This is all about winning the allegiance of the population.
"The allegiance is not won in a day it must be won over time. It cannot be forced."
Speaking at a press briefing at the Ministry of Defence's Whitehall headquarters the operation "cannot be seen as a campaign of us versus them [the Taliban]", although "it is absolutely about removing their ability to operate in areas".
Earlier, the commander of the British forces in Afghanistan, Brigadier James Cowan, said the aim was to "not to crush the Taliban but to win the people".
Soldiers from the Grenadier Guards Battle Group, Coldstream Guards and the Royal Welsh are taking part, along with the Helmand Provincial Reconstruction Team and the Operational Mentor and Liaison Team.
The UK soldier who died was one of two Isaf service members who died in southern Afghanistan on Saturday as part of the operation.
And three US soldiers were killed by an improvised explosive device just hours after the offensive was launched, although it is not yet clear if they were part of Operation Moshtarak.
Nato forces participating in the operation seek the allegiance of locals
The Afghan army said 70% of Marjah had been cleared and 20 militants killed, according to its regional commander.
Nato Commander Maj Gen Nick Carter said 11 Taliban bases had been captured and the offensive had been "so far extremely successful".
Speaking to BBC Radio 4's Today programme, he said: "In terms of the overall insertion - and I prefer to use the word insertion rather than assault - it's gone remarkably well," he said.
In an eve-of-battle speech to troops at Camp Bastion, Brig Cowan urged them to remember they were fighting alongside their Afghan partners and other allies.
"In the past few weeks we have trained to be a combined force. Soon we will be part of an operation the like of which has not been seen since the start of this campaign."
Brig Cowan urged his troops to avoid civilian casualties at all costs, even when confronted with grave danger.
'Heart of darkness'
He said: "Defeat the enemy by avoiding civilian casualties. Hold your fire if there is a risk to the innocent, even if this puts you in greater danger. That kind of restraint requires courage - courageous restraint. This you have shown throughout our time in Afghanistan.
"Offer an open hand in friendship to those who do not wish to fight. They can join the people of Afghanistan and their government in rebuilding their society.
"For those who will not shake our hand they will find it closed in a fist. They will be defeated."
Earlier this week British forces began a "softening up" process, taking part in a Nato ground and air offensive on insurgent positions.
On Thursday a British soldier involved in Operation Moshtarak was killed by an IED, and Defence Secretary Bob Ainsworth has warned that there will be more casualties in the coming days.
Speaking earlier on Friday, the Commander of the British Engineer Group in Afghanistan warned troops: "We are going into the heart of darkness."
Lieutenant Colonel Matt Bazeley, the Commanding Officer of 28 Engineer Regiment, told soldiers "it is bloody dangerous out there," but added "this is what you have been trained for".
The MoD said Moshtarak was the first part of a three-stage plan to increase security in Afghanistan.
OPERATION MOSHTARAK: DAY ONE - 13 FEBRUARY 2010
1: Consolidation of security
2: UK/Danish troops disrupt Taliban movements
3: Forces secure Canal 56 crossings
4: Helicopter insertions
5: Helicopter and ground insertions into Marjah
Source: UK Ministry of Defence