Mae Sot, Thailand (CNN) -- Thousands of people have begun returning home to Myanmar from Thailand, after learning that post-election violence has wound down, the Thai military said Tuesday.
About 10,000 refugees had poured across the border on foot and on inner tubes across the Moei River to flee fighting that erupted between soldiers of the Myanmar government and the rebel Democratic Karen Buddhist Army.
By Tuesday, fewer than 5,000 refugees appeared to remain at a camp set up just across the border, in Mae Sot, Thailand. Many people were crossing the Moei River back into Myanmar, which is also known as Burma.
"The number of refugees should now be less than 10,000 in Mae Sot, since there are many of them who have left Thailand voluntarily this morning, as they learned that the fighting was over in Myawaddy," said Lt. Gen. Wannathip Wongwai, the Thai 3rd Region army commander.
Some refugees told United Nations staff that had felt their lives were at risk after their houses were attacked in the fighting. They escaped with only their children -- some newborn babies -- and only the clothes on their back. Some were even barefoot, according to the U.N. High Commissioner for Refugees (UNHCR).
UNHCR said it provided 90 tents and plastic sheeting for shelter. It said the Thailand Burma Border Consortium, which provides food and shelter to about 150,000 refugees already living in nine camps in Thailand along the Myanmar border, provided food to those who fled the latest fighting.
Soe, a refugee who declined to reveal his full name fearing government retribution, said a friend called him Tuesday to let him know the situation had quieted down.
"I have been here for two days already and I'm going back to my home today," he said.
Thailand was trying to speed the refugees' return.
"The Thai authority is now coordinating with the Burmese Myawaddy governor and concerned authorities to open the border bridge to allow those who are willing to go home voluntarily," Wannathip said.
The rebels and forces from the Myanmar government clashed Sunday and Monday over control of the town of Myawaddy, which sits across the Moei River from Mae Sot. The Thailand-Burma Friendship bridge connects the two towns.
Wannathip said military officials from Myanmar told him they had retaken control of Myawaddy late Monday afternoon, after bringing in 500 reinforcements to battle the Karen splinter group.
At least five Myanmar refugees and five Thais were injured in the fighting, the officials said.
A mother with a baby told CNN on Tuesday, "I was so frightened when I heard the bombs and gunfire, I grabbed anything I could and ran to Thailand." She, too, did not give her name.
According to a report on the website Burma Election Tracker, the clashes began when Karen militia members who had been employed as government border security troops rebelled because the Myanmar military was forcing people to vote at gunpoint in the past weekend's election.
"In order to win votes in the elections, [the junta] is bullying and forcing people to vote. But the people want to boycott [the vote], so the soldiers are holding them at gunpoint and our troops had to intervene and take sides with the people," the website report quoted Brig. Gen. Na Kham Mwe, head of the breakaway Karen faction, as saying.
Polls closed Sunday in Myanmar's first election in 20 years, which critics have called a facade of democracy orchestrated by the ruling military junta. It has not released election results, but critics say the outcome is all but certain to favor the regime.
Opposition parties were either limited in the candidates they could put on the ballots or boycotted the election altogether. The junta did not allow international monitors.
The Karen ethnic minority in Myanmar is divided into two main groups: Buddhists who support the ruling junta and Christians who do not. Those behind Monday's clashes have split from the pro-junta group.