Between 200 and 300 civilians had fled the fighting in the area, it said.
The two children were killed when a vehicle they were travelling in was caught up in a gun battle, said General Mohammad Zahir Azimi, adding five civilians were also wounded in the incident.
The Nato soldier was reportedly killed by a landmine.
Musa Qala had become a base for "foreign terrorists," Azimi said.
"Hundreds of terrorists had massed there."
However, A Taliban spokesman downplayed its importance as a base.
Qari Mohammad Yousef Ahmadi told Al Jazeera: "Musa Qala is not the only district for our Mujahideen to be there, we have bases in other districts that are still in our control".
The Taliban took control of Musa Qala in February and the town and the region around it have seen heavy fighting this year.
"Afghans want peace and security, the Afghan people are neither terrorists or support terrorism"
Haji Fazel Mohammad, a Panjwaii elder
A deal which saw British troops hand control of the area back to tribal elders lasted only a few months before the Taliban returned.
They briefly imprisoned the elders.
Afghan and international troops have been keeping a watchful eye on Musa Qala ever since.
Speaking to Al Jazeera on Saturday, Lutfullah Mashal of the Security Council of Afghanistan said: "The Afghan nation army is the lead element in this operation.
"We are sure that with the co-operation of the local tribes, the Afghan national forces will be able to recover the area from the foreign terrorists who are holding the people of Musa Qala hostage."
Meanwhile, in the Panjwaii district of the southern Kandahar province, Nato's International Security Assistance Force (ISAF) gave tribal elders an ultimatum on Friday.
In a meeting in which local police were present, Canadian ISAF forces told tribal leaders that if they wanted assistance with security and reconstruction, they must reject the Taliban.
Major Patrick Robichaud, a spokesman for Isaf's Canadian forces, said: "We are now coming up to this crossroad, where they need to let go of one side and accept the protection of the government and the Isaf forces."
Robichaud said development agencies wanted to begin projects in the area but could turn elsewhere if security issues were not resolved.
However, Afghan leaders told Al Jazeera they felt trapped by the choices, fearing the Taliban would retaliate if they accept the Canadian offer.
Haji Fazel Mohammad, a Panjwaii elder, said: "Afghans want peace and security, the Afghan people are neither terrorists or support terrorism.
"Instead of giving an ultimatum to the elders of Panjwaii, they should give this ultimatum to Pakistan."