The head of the UK's armed forces, Sir Jock Stirrup, has said the killing of 12 civilians during Operation Moshtarak in Afghanistan was a "serious setback".
No British troops were involved when two rockets fired by coalition forces missed their target in Marjah.
Sir Jock said Britain must focus on regaining the Afghan population's trust but that accidents were "inevitable".
Gordon Brown says he told Afghan President Hamid Karzai everything was being done to minimise civilian deaths.
The prime minister also said UK commanders had indicated they had "all the equipment they needed" for the offensive, involving up to 15,000 Nato troops searching for the Taliban in Marjah and Nad Ali.
On the third day of the operation, the chief of the defence staff told BBC Radio 4's Today programme the population would be safer under the Afghan government than the Taliban.
He said: "It is always damaging, but of course in any conflict situation accidents happen and we must remember that most of the civilian casualties... are caused by the Taliban.
"In 2009, nearly two thirds of the people who died as a result of improvised explosive devices were actually civilians and aid workers so it is not the case that under the Taliban the civilians are safe," he said.
He said it could take up to 12 months before the operation could be deemed a success and it was not about "battling the Taliban" but "about protecting the local population and you don't protect them when you kill them".
He added: "This a very challenging operation. Time is important and it is going to take time for us to persuade the locals that they should be accepting the Afghan government."
The prime minister said he was confident the offensive would succeed.
"We will break the Taliban during this enterprise because people do not want to have the fear that is created by the Taliban and the possibility of al Qaida coming back into Afghanistan," he said.
"I have spoken to President Karzai and I wanted him to know that we are doing everything in our power to minimise civilian casualties."
Speaking on a BBC Radio Suffolk phone-in during a visit to East Anglia, Mr Brown told listeners: "We are better equipped than ever we have been as armed forces.
"Before we had this latest exercise... the chief of the defence staff phoned the commanders on the ground asking them if they were absolutely sure they had what they needed to do the work."
The BBC's Ian Pannell, who is embedded with British troops, said the UK forces were still looking for roadside bombs and had held several meetings with local people in Nad Ali.
BBC security correspondent Frank Gardner said many insurgents in these areas are thought to have laid down their weapons or retreated north towards Sangin but home-made bombs have been planted in far greater numbers than Nato expected.
L/Sgt David Greenhalgh, of 1st Battalion Grenadier Guards, died in an explosion while on vehicle patrol as part of the operation, near Lashkar Gah on Saturday.
Since then, three other British soldiers have been killed in incidents unrelated to the offensive.
The Ministry of Defence said the first stage of the offensive in southern Afghanistan, which involved 1,000 UK troops, had gone to plan.
Maj Gen Gordon Messenger has said British troops, working with Afghan forces, have come under small-arms fire but "nothing had stopped the mission progressing".
He said soldiers from the Royal Welsh Regiment, working with Afghan forces, had uncovered 13 improvised explosive devices (IEDs) and military tunnels.
Meanwhile, work had begun to build bridges over canals and create temporary bases in the area.
Lindy Cameron, the British government official in charge of the Provincial Reconstruction organisation in Helmand, said if Moshtarak was successful her team would move swiftly into Marjah.
"The first thing we'll do is basically support the government to repair any damage that's been caused in the conflict," she said.
"The key issue actually is to make sure that the government is out there talking to people in the district about what it is that they want."
Operation Moshtarak - which means "together" in the local Dari language - is the biggest Afghan mission since the 2001 invasion.
It is being led by 4,000 US Marines, supported by the Afghan National Army and British, Canadian, Danish and Estonian troops.
More than 1,200 British troops are currently involved on the ground, with a further 3,000 available if needed.
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.