MAE SOT, THAILAND (REUTERS) - Myanmar's oldest rebel force wants international help to establish a "no-fly zone" near the Thai border, after warning there was a danger of clashes with the army resulting in civilians being targeted by air strikes.

There has been an escalation in fighting recently between the army and the Karen National Union (KNU), prompting thousands of people to seek refuge in Thailand.

About 3,400 people have taken shelter in Thailand over recent days, Thai authorities said. Thousands more are stranded on the Myanmar side of the border, waiting to cross.

In a statement released this week, the KNU warned of a "high possibility" of military air strikes on civilians.

"These air strikes won't target military bases but civilian bases as in schools, hospitals, houses and villages," the head of the KNU's foreign affairs department, Mr Saw Taw Nee, told Reuters, citing his experience from previous bouts of fighting.

A spokesman for Myanmar's military junta did not answer calls seeking comment.

The KNU urged the international community to identify a no-fly zone by seeking an emergency meeting of the UN Security Council.

Last month, the UN Security Council, in a rare statement that was agreed by its 15 members, expressed concern over violence across Myanmar and urged the military to exercise utmost restraint.

International efforts to end the conflict in Myanmar since a February coup have been limited to diplomatic initiatives and attempts to exert economic pressure through Western sanctions.

Since the military overthrew the civilian government led by Aung San Suu Kyi, the Assistance Association for Political Prisoners (AAPP) has said that more than 1,300 people have been killed by the security forces.

The military has said the figures from AAPP, a monitoring group cited by the United Nations, are exaggerated.

The KNU agreed to a ceasefire in 2012, ending an insurgency for self-determination that began soon after Myanmar gained independence in 1948, but its forces have been clashing with the army since the coup and it has allowed opponents of the coup to take shelter in territory it controls.

The latest fighting had been triggered by the army's attempts to arrest people in the Lay Kay Kaw area, said Mr Saw Taw Nee.

"They came and checked on the town which we allow. However, they didn't keep their promise and arrested people which we totally don't accept," he said.

The KNU said three of its fighters and 15 government soldiers had been killed in the clashes. Reuters could not independently verify the account.