Brigadier-General Eric Tremblay, a Nato spokesman, said that most of the objectives of Operation Moshtarak had been achieved.
'Pockets' of resistance
Tremblay said that troops from the 15,000-strong joint Afghan, Nato and US force were now responsible for clearing the last "pocket" of resistance in the western part of Marjah.
"Perhaps the pocket in the western side of Marjah still gives freedom of movement to the Taliban, but that is the extent of their movement," he said.
Al Jazeera's James Bays, reporting from Helmand, said the "low military progress and the fact that they still have to clear a lot of area of mines" would make it hard to install a government.
"There's another reason why it's hard: the government that is supposed to roll is not quite ready to roll," said Bays.
"The Afghan local government isn't the most sophisticated machine anyway ... [and] Marja is not itself a district at the moment in terms of the local government map of Afghanistan."
US marines and Afghan troops in Marjah "saw sustained but less frequent insurgent activity" on Wednesday, limited mostly to small-scale attacks, Nato said in a statement.
Mohammad Gulab Mangal, the governor of Helmand, who was among those who watched the flag-raising on Wednesday, said that life was beginning to return to "normal" in Marjah.
"You can see the people are busy in their daily lives. Some shops are still closed but once they arrest the enemy, hopefully, the shops will reopen too," he said.
Mangal said Afghan troops were still active in the area, and he declined to give an estimate for how long it would take until Marjah was under complete government control.
"From the military point of view, one cannot set an exact timeline but work to clear mines continues," he said.
Afghan and US troops said the Taliban fighters holding out in Marjah were using civilians as human shields.
They said the fighters were firing from compounds where US and Afghan forces could clearly see women and children on rooftops or in windows.
But our correspondent said the the "majority of the Taliban in Helmand are people from Helmand, they are ordinary people from Helmand who have taken up arms against the foreign forces ... that have come to invade their country".
"These Taliban fighters live with their families and their children," Bays said.
"So, although it's been seen in Western eyes as using human shields - and I know that the Taliban are quite aware of the rules of engagement the international forces have - they know they have to try and avoid any civilian casaulties.
"But in Afghan eyes some would see this as a Taliban fighter in his home with his family trying to protect that family and that home."
Nato forces say the offensive, in which 15 Afghan civilians have died, is aimed at re-establishing Afghan government control so security and civil services such as police stations, schools and clinics can be set up.
Officials have reported the deaths of only two international forces troops during the operation so far, with one American and one Briton killed on Saturday.