It is the first such large-scale operation since US President Barack Obama authorised the deployment of 17,000 extra US troops to Afghanistan, as part of a new strategy for winning the conflict.
Many of them are being redeployed from operations in Iraq, to help with training Afghan security forces and to tackle the insurgency.
Meanwhile the US military reported that a soldier had been captured by insurgents in eastern Afghanistan on Tuesday. He was not part of the current operation.
Lack of capacity
The offensive is the marines' first major operation since their recent deployment to Afghanistan.
Caroline Wyatt BBC defence correspondent
The US marines say the operation will be decisive and is intended to seize almost the entire lower Helmand River valley, which remains the heartland of the Taliban insurgency in Helmand and a major area for the production of opium, which helps fund the insurgency.
US commanders hope this offensive will help turn the tide in the current stalemate against the Taliban. The aim of this major operation is to "clear, hold and build" in areas under Taliban influence ahead of Afghan presidential elections this August.
The hope is also that if US and other Nato forces are seen as clearly winning the military battle against the insurgents, middle and lower-ranking Taliban leaders and fighters are more likely to defect back to the Afghan government's side, with US and UK sources in Kabul convinced that the US troop surge is already unsettling the Taliban leadership.
The operation - codenamed Khanjar or Strike of the Sword - began when units moved into the Helmand river valley in the early hours of Thursday.
Helicopters and heavy transport vehicles carried out the advance, with Nato planes providing air cover.
The BBC's Martin Patience in Kabul says the idea is that they will move into towns and villages which are under Taliban control.
With the fresh US deployments, military commanders say they are confident that they will make "significant" gains this summer, even if, as our correspondent says, a decisive victory is unlikely.
UK-led forces in Helmand launched their own operation to combat the Taliban insurgency last week, in what the Ministry of Defence described as one of the largest air operations in modern times.
Thousands of British forces under Nato command have been fighting the Taliban in Helmand since 2006, but there has been criticism that they have been overstretched and under-resourced.
Two British soldiers were killed in an explosion in southern Afghanistan on Wednesday, the UK Ministry of Defence reported.
Southern Afghanistan is considered a Taliban stronghold.
"Where we go we will stay, and where we stay, we will hold, build and work toward transition of all security responsibilities to Afghan forces," said Brig Gen Nicholson in a statement.
At a briefing at the US military's Camp Leatherneck last week, he told personnel and embedded reporters: "One of the most critical things is to tell people why we're there, and we are going to have a limited opportunity to gain their trust."
The security forces will build bases to provide security for the local people so that they can carry out every activity with this favourable background, and take their lives forward in peace
The operation aims to improve security ahead of presidential elections on 20 August, allowing voter registration where before there was none, Gen Nicholson said.
A US military spokesman, Captain William Pelletier, told the BBC there had been "no enemy contact" in the first hours of the operation, but one marine was slightly injured when an improvised explosive device detonated in the village of Nawa.
Nawa and nearby Garmsir - near the provincial capital Lashkar Gah - are key targets in the operation, as the area is considered a refuge for militants and no US or Nato troops have previously operated there in large numbers.
Capt Pelletier said the US military was prepared for casualties, but stressed that "it is absolutely essential that no civilians be harmed".
Helmand Governor Gulab Mangal predicted the operation would be "very effective".
"The security forces will build bases to provide security for the local people so that they can carry out every activity with this favourable background, and take their lives forward in peace."
The Pakistan army, which is fighting its own battles with the Taliban, said it would redeploy some of its soldiers to the Chaman area bordering Helmand.
But spokesman Maj Gen Athar Abbas told the BBC that no additional troops were being sent to the region.
"Basically, it's a rearrangement of troops already present there," he said.
"It's in anticipation of movement from the other side. The area of the rearrangement is the one around Chaman in Baluchistan."
The BBC's Shoaib Syed Hasan in Islamabad says the rugged terrain makes the border almost impossible to police, and though Pakistan regularly deploys troops along the border to catch militants they are rarely successful.
As of June 2009, Nato's International Security Assistance Force had 61,130 personnel from 42 countries including the US, Canada, European countries, Australia, Jordan and New Zealand. The US is the largest contributor, providing 28,850 soldiers.
About 4,000 US and 650 Afghan troops deployed to Helmand river valley
Initial operations focused on villages of Nawa and Garmsir near the provincial capital Lashkar Gah
British operation recently recaptured the village of Babaji from the Taliban to the north of the region
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