Myanmar security forces have killed at least 510 people since the coup, with 14 shot dead on Monday including children and young people, advocacy group Assistance Association for Political Prisoners (AAPP) said.

'We don't want to have any influx into our area'

The KNU said 3,000 people crossed the Salween River into Thailand, fleeing the military's aerial bombardments, and 2,000 were pushed back.

Activist group the Karen Women's Organization (KWO), which operates within Karen state and refugee camps in Thailand, confirmed the air strikes had forced 10,000 people in the state from their homes, and 3,000 had crossed into Thailand.

CNN has not been able to reach Thai authorities for comment, but Reuters cited Thichai Jindaluang, the governor of Thailand's Mae Hong Son province, denying refugees were being pushed back.

When CNN reached out to Thailand's Foreign Ministry, they directed us to a statement published by local media from the ministry spokesman, Tanee Sangrat, saying, "Those reports cite information solely from non-official sources without confirming the facts from official sources on the ground which affirmed that no such pushback took place."

On Tuesday, Thailand's Prime Minister Prayut Chan-o-cha said officials had not forced refugees back to Myanmar, but they had spoken with some of the people who had entered Thailand.

"After we asked questions (such as) what are their problems in your country, they said, 'there's no problem.' So, since there is no problem, can they just return home for the time being? We didn't force them (to return) with guns, we even shook hands and blessed them good luck," Prayut said in a media briefing.

"We have to take care of them based on humanitarian principle. We have a lot of experience... There is no way we will push them back if the fighting is still ongoing. But if there is no fighting now, can they return to their home?"

On Monday, Prayut said his government did not want refugees to cross the border but were preparing for a potential influx.

Myanmar is a 'conflict zone'

Thailand has hosted tens of thousands of refugees in nine main camps along its border with Myanmar for three decades, following armed conflicts, human rights abuses and persecution of ethnic minorities by the Myanmar military.

Most of those who crossed the border over the weekend are from Mu Traw district, where the bombing has been concentrated. Many of those are people who have already fled their homes and are living in the Ei Tu Hta displacement camp.

Photos provided to CNN by the KNU purport to show Myanmar refugees being denied entry into Thailand. And video shot by a Karen villager and published by Reuters showed refugees boarding boats under the watch of Thai soldiers.

Armed rebel groups have been fighting the Myanmar military on and off for the past 70 years in the country's ethnic states but fighting in some areas has increased since the February 1 coup.

The KNU said three civilians were killed in the strikes, which began on Saturday and continued into Monday. Military jets also killed at least two members of the KNU militia Saturday.

David Eubank, founder of the relief organization Free Burma Rangers, said it was the first time in 20 years that airstrikes had been carried out in the area.

Despite the government's denials, several human rights groups have criticized the Thai authorities.

"Forcibly sending people back into a conflict zone amounts to refoulement and is against international refugee law," said the European Karen Network, a group of Karen communities from several countries in Europe, in a statement Monday.