Colombo said that fighting between Tamil Tiger fighters and the military had stopped.
A spokesman for the office of Mahinda Rajapakse, the Sri Lankan president, said on Thursday: "We started the process today in a big way because the fighting has died down in those areas."
Officials said that about 10,000 Muslims had been moved out of relief centres within the district and were taken home.
"Two refugee welfare centres closed today and seven more are functioning, but they have less than 5,000 people in them. More civilians want to return," a district official said.
Although the government says Muttur is now safe, local NGOs are concerned about the living conditions and security of residents there.
Mafaz Nijam, aid organiser with Jamaath-e-Islami, a Sri Lankan Muslim foundation, who has been stationed with 14,000 refugees at Pearathuweli camp in Kantale, told Aljazeera.net: "Although the government has said that Muttur is safe, our main concern is whether people will be able to return to their normal lives as no official resettlement process has started yet.
"I believe that the basic infrastructure such as electricity and water is back on in Muttur. And the security situation seems to be stable"
Rukshan Ratnam, information manager at the IFRCRC
"We are also concerned that the government is compelling people to go back when we are not sure what the situation with their homes is. Houses are not repaired, and the psychological effect of the war also needs to be addressed. People are psychologically disturbed."
The displaced were rounded up onto buses by government forces and told they were going to return to Muttur.
Rukshan Ratnam, information manager at the International Federation of Red Cross and Red Crescent Societies (IFRCRC), Sri Lanka delegation, told Aljazeera.net: "I believe that the basic infrastructure such as electricity and water is back on in Muttur. And the security situation seems to be stable."
During the one-month of fighting, shops and homes were looted in the town.
The phones at the Jamaath-e-Islami offices in Muttur were not working properly on Thursday.
The government has guaranteed
that Muttur is safe
Nijam told Aljazeera.net that there are many residents who move from their homes, where they stay during the day, back to camps such as the Al Hilal camp in Muttur at night because they do not feel safe at home.
Up to 40,000 civilians were forced to flee Muttur, just 10km across from Koddiyar Bay, when heavy fighting between the military and the Tamil Tigers broke out in August.
Five families remain in the Pearthuweli camp, which Nijam says will close tomorrow.
"There are five families still in the camp. They are from Topur, which was the scene of some shelling yesterday. They are too afraid to go back," he said.
Reto Meier, the International Committee of the Red Cross (ICRC) delegate-general for Asia and the Pacific, said after a visit to Sri Lanka that Jaffna was "choking", having been cut off along with Vanni, from the rest of the country for more than three weeks.
"What can we do? We have to continue to work, sometimes you have to make sacrifices"
Jamaath-e-Islami aid worker
"The flow of goods and people across the lines separating government-controlled from LTTE-held territory has come to a virtual standstill in the north owing to restrictions imposed by both sides," he said.
The LTTE is the Liberation Tigers of Tamil Elam.
He urged both sides to stop fighting so that a corridor for aid could be secured to the peninsula.
Seventeen local aid workers from Action Against Hunger, a French charity, were shot dead at Muttur in early August in an execution style killing.
Although, the Sri Lanka Monitoring Mission released a report only last week holding government security forces responsible for the killings, Sri Lankan-based NGOs have continued their work.
"What can we do? We have to continue to work, sometimes you have to make sacrifices," said Nijam.