US special forces are also working with Afghan commandos around the Baramsha border crossing with Pakistan, in an attempt to cut off the Taliban's main supply route.
Since the start of July, 40 foreign soldiers have died, including four killed "as a result of improvised explosive device (IED) strikes from insurgents" on Saturday, officials said.
Qari Yousef Ahmadi, a Taliban spokesman, told Al Jazeera on Sunday: "We have been successful. The enemy has been suffering heavy casualties.
"It is a guerrilla war and those are our tactics. We will resist them in Helmand, and will attack them all over Afghanistan."
A high-ranking government source in Helmand told Al Jazeera that the offensive was proceeding slowly, and in central Helmand, the enemy was in fact much stronger.
Zeina Khodr, Al Jazeera's correspondent in Kabul, said: "The Taliban has been ambushing troops; they have been laying improvised explosive devices and roadside bombs. So, the [coalition forces'] advance really is slow."
"This is a guerilla war, it is not going to end soon and it is highly unlikely that the Taliban will give up territory such as Helmand, such a strategic area."
"A Taliban spokesman told us that the outcome of this operation 'would tell us who is actually the man, and who is the woman'," our correspondent said.
Diplomacy and development
President Obama said the US and its allies needed to combine their military efforts in Afghanistan with diplomacy and development "so that Afghans feel a greater stake and have a greater capacity to secure their country".
|Obama said Afghanistan's police and army needed development after the poll [AFP]
After Afghanistan's planned election next month, "we need to start directing our attention to how do we create an Afghan army? An Afghan police? How do we work with the Pakistanis effectively so that they are the ones who are at the forefront of controlling their own countries?" Obama said.
Al Jazeera's correspondent said this is something the Afghan officials have been saying for months, if not years.
"The US still needs to develop the Afghan security forces, and that will take some time."
"Government forces lost the district of Nuristan on Thursday because they didn't have enough local security forces," our correspondent said.
"The governor at 5am [0030GMT] this morning confirmed that they had regained that district from the Taliban, but holding it will be a difficult fight."
Helmand province, where the US is joined by around 6,000 British forces, is the source of most of Afghanistan's opium crop - the world's largest - which finances the Taliban.
Zahir al Azimy, an Afghan defence ministry spokesman, told Al Jazeera: "Once we take over an area where there is poppy cultivation, we cut off the Taliban's revenue."