The KNU said that Ler Per Her camp in Myanmar, which sheltered internal refugees, was abandoned last week, prompting one of the largest refugee movements into Thailand in recent years, and that government forces were trying to overrun five Karen positions in the area of the camp.
The Free Burma Rangers, which helps displaced people in eastern Myanmar, said on Wednesday that government troops had overrun three of those positions.
The refugees are taking shelter about 100km north of Mae Sot, a border town located 380km northwest of the Thai capital, Bangkok.
But David Thaw, a KNU spokesman, told the Associated Press that the rebels have largely repelled the offensive and "killed or wounded 148 soldiers'' in recent weeks.
He also said that five Karen fighters have been killed in the fighting.
It is impossible to independently verify the claims because reporters cannot access the area and the Myanmar government has not responded to requests for details of the fighting.
But on Thursday, state media in Myanmar said the "so-called refugees'' fleeing into Thailand were not ordinary villagers but Karen fighters and their families from five KNU brigades.
Some 100,000 mostly Karen refugees already shelter in camps in Thailand after fleeing the violence over the past two decades, while aid agencies say nearly half a million others are internally displaced inside eastern Myanmar.
Human rights groups as well as the United Nations have long accused the Myanmar government of torture, killings and rape of Karen civilians in their attempts to stamp out the insurgency.
The military government denies such allegations.