About 4,000 marines, backed by Nato aircraft and a 650-strong Afghan force, are moving into towns across Helmand.
They have reportedly faced little resistance so far, despite the Taliban vowing that the thousands of fighters it has in the area would fight back.
However, the four-vehicle convoy of a private security company did come under attack in Helmand's Gereshk district on Saturday.
One security guard was killed and four others were wounded after a suicide bomber detonated an explosives-packed vehicle near the convoy, Daud Ahmadi, a spokesman for the provincial administration, said.
Two Afghan soldiers were also killed in a bomb blast in Musa Qala district on Friday, the interior ministry said.
General David Petraeus, the US chief military commander, has warned that the battle for control over the province will be a "tough fight".
"I think you have to recognise this is an enemy that is adaptable and at times is barbaric," he said during a visit to Canada.
"[They] adjust to our tactics, techniques and procedures. We certainly do see it as an enemy that represents an ideology that does not tolerate those who do not think the way they do."
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.
Suspected Taliban fighters have also continued to strike far away from the offensive, killing at least two US soldiers in an attack on a military base in the Paktika province of eastern Afghanistan on Saturday.
Lieutenant-Commander Christine Sidenstricker, a US military spokeswoman, said that the attack on the base in Zirok district had also wounded another seven US troops and two Afghan soldiers.
"It was a complex attack that started with small-arms and indirect fire on the post, then an improvised explosive device went off," she said.
|The military operation is the biggest by the
US marines since the Vietnam war [AFP]
Hamidullah Zhwak, a spokesman for the local administration, said that the US casualties occurred when a fuel tanker exploded.
He said the troops called in helicopters after being attacked and the retaliatory air raids killed at least 32 Taliban fighters.
"After the blast, the American helicopters came in and attacked the Taliban who were preparing to attack the district headquarters," he said.
Zabiullah Mujaheed, a Taliban spokesman, claimed responsibility for Saturday's suicide blast.
"Today Hafiz Omar carried out a suicide attack with 8,000 kilos of explosives in a tanker on an American base," he told the AFP news agency.
"At the same time 100 mujahidin [fighters] attacked the base just after the explosion ... Americans suffered heavy casualties and we lost five of our fighters."
The attack came in the same area where a US soldier, who has been missing since Tuesday, is believed to have been captured by pro-Taliban fighters.
Elsewhere in Afghanistan, seven policemen were killed and two others injured after their vehicle hit a roadside bomb in Registan district in southern Kandahar, the interior ministry told Al Jazeera.