Al Jazeera's Zeina Khodr, reporting from Lashkar Gah, said that the governor of Helmand province was confident that the operation would succeed, but the Taliban were as defiant as ever.
"They are denying that the marines as well as the Afghan national army are in control of Khanishin," she said.
"They are saying the US marines only control one hill and that they have decided to confront them. Even if they control a certain number of villages, they will not be able to keep them."
The US offensive is the first big push to drive the Taliban out of the province since Barack Obama became the US president in January.
The Taliban has vowed thousands of its fighters in the area will fight back, but a military spokesman said that there had only been limited resistance so far.
Up to 4,000 marines, backed by Nato aircraft and a 650-strong Afghan force, are moving into towns across Helmand.
Pentagon officials have said that the plan - the largest offensive by the US marines since Vietnam - is not just to inflict casualties against the enemy, but to dig in and hold on to territory.
"We're gonna go there and go to the far reaches where the Taliban is not looking for us, where they're not expecting a fight, where they're not sitting in prepared defensive positions and that's gonna keep them off-balance," Captain Zachary Martin, a spokesman, said.
US forces and the Afghan National Army commanders say they have adopted a new strategy that aims to engage local communities and convince them they are there to make their lives better, rather than simply leaving areas after the battle.
Khodr said: "... the president of the country, as well as provincial officials, have been sending messages to tribal elders promising them that they will stay until they can ensure peace, stability, security... and change their lives for the better."
Helmand is one of the Taliban's main heartlands in southern Afghanistan and produces the largest share of the country's opium crop, which supplies about 90 per cent of the world's heroin.
Jonathan Owen, a military analyst and former US marine, told Al Jazeera that the operation was significant as it marked the first time US and Afghan military forces were going to areas previously "untouched by coalition forces in any sizeable manner".
US commanders have described combat situation in the southern province - Afghanistan's biggest - as a stalemate
Provincial officials estimate four out of Helmand's 13 districts are under Taliban control
Some 9,000 British troops along with other Nato forces have been based there since 2006 but have struggled with the size of the area and difficulty of the terrain
The region is home to mainly Pashtuns, the country's largest ethnic group
More than half of Afghanistan's opium - which make up about 90 per cent of the global supply - is cultivated in Helmand, according to the UN drugs agency, a key source of funds for the Taliban
"It's going to be significant especially because of the impact it can have on the Taliban. This area produces about 50 per cent of the opium production worldwide," he said.
"Any incursions the US marines make are going to directly affect that and that's going to directly impact the funding and ability for the Taliban to carry out operations."
Despite the new offensive in Helmand, Admiral Mike Mullen, the chairman of the US joint chiefs of staff, told Al Jazeera that the US had not ruled out the possibility of talks with the Taliban.
"I think that at some point in the long-term [the Taliban] will become part of the political process," he said.
"That said, I don't think that is near at hand from anything I have seen - not unlike other insurgencies - where that routinely happens at some point in time.
"At some point they will put their arms down and they will come into the process. They will look at other opportunities that they don't have right now.
"The specifics of exactly how that is going to happen and when it is going to happen are yet to be determined, but overall, I think that is the path," he said.
He warned, however, that as with "any insurgency … you have a hardcore group that you are never going to turn around, and who are going to have to be killed or captured somehow.
"Then you end up dealing with the vast majority of the rest of an insurgency".
The US military also on Friday disclosed that an American soldier who went missing earlier in the week in Paktia province had been captured by Taliban fighters.
"We are using all our resources to find him and provide for his safe return," Captain Elizabeth Mathias said on Thursday.
The military operation in Helmand province comes in the run-up to Afghanistan's presidential elections planned for August 20.
US and Nato commanders have said they intend to seize Taliban-held territory in the south in time for the polls.
The US has sent 8,500 marines to Helmand in the last two months, the largest wave of a massive build-up of forces that will see the number of US troops in Afghanistan rise from 32,000 at the beginning of this year to 68,000 by year's end.
The operation is a test of Obama's strategy to train the US military's focus on Afghanistan and Pakistan instead of Iraq, on the premise that the Taliban challenge is the main security threat facing the US.