The statement by the UN Assistance Mission in Afghanistan (UNAMA) came as clashes between government forces and the Taliban in Lashkargah, the provincial capital, and surrounding areas continued for a sixth consecutive day on Thursday, TOLO News reported.
According to the Defence Ministry, at least nine people were killed when two Afghan National Army (ANA) MI-17 helicopters "crashed due to technical issues" in Nawa district.
The Ministry added that 23 Taliban militants have been killed so far since the group launched the attacks over the weekend.
Reacting to the continuing violence, the UNAMA said that the violence "unleashed in Helmand this week has forced thousands of Afghanistan civilians to leave their homes and initial reports suggest civilians have been killed and injured, including women and children".
"The number of civilians killed and injured, a key indicator of the intensity of violence, has so far been lower in 2020, but in recent weeks a worrying reversal seems to be emerging.
"Civilians are routinely killed or injured in armed clashes with high casualties resulting from indirect weapons: mortars, rockets, grenades. These civilians, including many children, must be protected from harm.
"The only way to do that is to stop the violence," it added.
Taking to Twitter, the US Charge d'Affaires Ross Wilson, said: "I stand behind UNAMA's call to protect civilians in Helmand, who should have safe passage to leave dangerous areas. It is indefensible that the Taliban continues to put civilians at risk through needless violence. Afghanistan needs peace now."
The UK embassy in Kabul also condemns the Taliban offensive, saying: "We continue to support the ANDSF and the brave efforts made to create lasting peace and stability in Afghanistan."
The violence comes as contact groups from both sides of the Afghan negotiations resumed their meetings on Monday to seek an agreement on procedural rules intended for the formal talks, TOLO News reported.
On Wednesday evening, a general meeting of chiefs and delegates from both the Islamic Republic of Afghanistan as well as the Taliban was held, said Nader Nadery, a delegate from the government's side.
Also confirming the meeting, Taliban spokesperson Mohammad Naeem in Doha said contested points were discussed and contact groups were instructed to resolve the dispute as soon as possible.