The UN's refugee agency on Monday called for Thailand to allow them "urgent access" to more than 3,000 Myanmar refugees who fled to the kingdom to escape fighting in conflict-wracked Karen state.
Clashes between Myanmar's military and the Karen National Union -- a rebel group vocally opposed to a junta which deposed a civilian government in February -- broke out last week in a town not far from the Thai border.
Some 700 refugees crossed the river into Tak province on Thursday, fleeing artillery shelling and small arms fire. By Monday, the number had ballooned to 3,900 due to continued fighting, the UNHCR said.
"UNHCR is concerned for the welfare of these civilians and has approached the Thai authorities with offers of assistance," it said in a statement.
"UNHCR and NGOs have requested urgent access to the refugees to ascertain and deliver to them the necessary humanitarian and protection assistance."
Provincial authorities said late Monday about 3,500 refugees remain in two locations on the Thai side, as dozens have gradually returned since fighting appeared to have ceased.
"Thai authorities are providing humanitarian assistance and transportation for those who volunteer to return to Myanmar by transporting them from the banks of Moei River," said a statement released by Tak province.
But Naw K'Nyay Paw, general secretary of Karen Women's Organisation, said the majority of people are still afraid.
"It's very tense and the fighting is still continuing in some areas," she told AFP. "I don't think it is representing the true feelings of the refugees."
The latest wave of some 1,500 people on Sunday came after renewed fighting broke out in Mae Htaw Thalay, a town bordering Mae Sot district of Tak province where displaced people were sheltering.
"There was artillery shooting in the area... The KNU tried to move them to a safer place," a Karen state resident told AFP, adding that thousands of displaced people, including children, were sent running as the shelling continued for hours.
"We heard shooting close to us and we tried to flee... We could only leave the village after they suspended shooting for a while around 7pm," he said.
Junta spokesman Zaw Min Tun confirmed the fighting in Mae Htaw Thalay on Monday, adding that the military are now "trying to control the situation by negotiating with KNU."
The clashes kicked off last week after state media reported junta troops entered KNU territory and arrested several dissidents, including a former lawmaker from Aung San Suu Kyi's ousted government.
The rebel group -- one of more than 20 ethnic armed groups holding territories in Myanmar's border regions -- has been a staunch opponent of the junta, providing shelter to anti-coup dissidents.