Reports from the international forces have been upbeat, but their advance in the area has been held up by bombs and booby-traps.
Zeina Khodr, Al Jazeera's correspondent in Kabul, said: "You hear Nato commanders as well as Afghan officials say that the operation so far has been a success. Yes, they're facing little resistance on the ground, but we have to remember that this has always been a Taliban tactic.
"Even though you hear their spokesmen saying all the time that 'we're going to face the invaders', and 'we're going to put up resistance', the Taliban knows very well that they cannot face a superior army.
"The Taliban spokesmen [are instead] telling us that one of the choices they have is simply to withdraw and use improvised explosive devices and mines - in fact, the whole area is booby-trapped.
"Commanders themselves are saying that they are advancing slowly because of the threat of such explosives."
US marines on Saturday led the charge on Marjah, a town of 80,000 in the central Helmand River valley controlled for years by the Taliban and drug traffickers.
The operation is the first major test of the new surge policy of Barack Obama, the US president.
At least 15,000 US, British and Afghan soldiers stormed the stronghold in what is also Nato's biggest operation since overthrowing the Taliban regime in 2001.
Troops dropped into Marjah from helicopters, immediately coming under fire and claiming their first Taliban victims within hours, Afghan army and US marine officers said.
Ali Ahmed Jalali, the former interior minister of Afghanistan, told Al Jazeera: "Marjah is a microcosm of the approach adopted by the international forces to clear an area and rebuild it and win the trust of the population.
"If the Marjah operations does lead to better stability in the area and if that is done properly, that will send a message to other parts of the country – but Marjah is only one of 385 districts in the country," he said.
British forces suffered their first casualty of the operation when a soldier was killed in an explosion while on a vehicle patrol in Helmand province's Nad-e-Ali area.
Nato's International Security Assistance Force (Isaf) said five foreign soldiers died on Saturday in the south of Afghanistan, three of them US troops, but did not say if they had been involved in the Marjah attack.
General Sher Mohammad Zazai, the commander of the operation's Afghan troops, said that at least 20 Taliban fighters were killed in the first hours of the assault.
"So far, we have killed 20 armed opposition fighters. Eleven others have been detained," he said.
Moshtarak puts into practice the new US-led counter-insurgency strategy combining the military objective of eradicating the Taliban with the need to replace their brand of harsh control with civilian authority.
Jalali, the former interior minister, said: "There's been a lot of progress in developing an indigenous capacity in the security force of Afghanistan, but they still need more time and training in order to be able to conduct operations independently."
Marjah is also a centre for opium production besides being a Taliban stronghold.
Hamid Karzai, the president of Afghanistan, has warned the troops to do everything possible to avoid harming civilians, a sensitive issue among war-weary Afghans.