Late on Thursday the US military announced the death of one soldier during the operation.
Separately, UK's defence ministry announced that one of two soldiers killed in an explosion the previous day in Helmand was the most senior British officer to have died in combat in Afghanistan.
Lieutenant-Colonel Rupert Thorneloe, 40, the commanding officer of the 1st Battalion Welsh Guards, died when a blast hit his armoured vehicle in a resupply convoy near the town of Lashkar Gah.
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.
Al Jazeera's Zeina Khodr, reporting from Kabul, said a similar offensive had been attempted in the same region in April last year, but US and UK troops pulled out afterwards and the Taliban moved back.
She said this time the "US forces say they will stay there and train local forces until they can take over".
"The Taliban say they are now launching a counteroffensive ... and say they have inflicted casualties along the lines of US troops," she said.
"US military officials have said there is some resistance and fighting.
"It is a strategic area, the Taliban get a lot of money from drug traders and can smuggle guns through the region ... [but] the Taliban say this is a war and they can move to another area.
"The US military know they have lost a lot of support among Afghans because of casualties among civilians ... they know this war cannot be won militarily and they are trying to show Afghans they are friends, not enemies."
Brigadier-General Larry Nicholson, the commanding officer of the Marine Expeditionary Brigade-Afghanistan, said "what makes Operation Khanjar [Strike of the Sword] different from those that have occurred before is the massive size of the force introduced, the speed at which it will insert and the fact that where we go we will stay, and where we stay, we will hold".
Run-up to vote
The military operation comes in the run-up to Afghanistan's presidential elections planned for August 20.
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
US and Nato commanders have said they intend to seize Taliban-held territory in the south in time for the polls.
Captain Bill Pelletier, a US military spokesman, said US marines launched a helicopter assault early on Thursday in the lower Helmand river valley.
The valley of irrigated wheat and opium fields along the river is largely in the hands of Taliban fighters, who have resisted British-led Nato forces for years.
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 in the former two were the main security threat facing the US.
Against the backdrop of the Helmand offensive, the US disclosed on Thursday that an America soldier who went missing two days earlier had been seized by the Taliban.
"We are using all our resources to find him and provide for his safe return," Captain Elizabeth Mathias said.
Our correspondent said it was the first time a US soldier has been held in captivity by an armed group in Afghanistan.