By Panu Wongcha-um, Poppy McPherson and Ananda Teresia

BANGKOK (Reuters) -Thailand's caretaker government is proposing to "fully re-engage" Myanmar's military rulers and has invited ASEAN foreign ministers to an informal meeting on Sunday to discuss a stalled peace plan, according to a letter seen by Reuters and sources aware of the invitation.

The proposal was made in a June 14 letter to Association of Southeast Asian Nations (ASEAN) counterparts from Thailand's Foreign Minister Don Pramudwinai, which was seen by Reuters on Friday and confirmed by three sources with knowledge of the planned meeting.

In a summit last month, ASEAN leaders called for an immediate end to the violence in Myanmar, which began after the military deposed the elected civilian government of Nobel laureate Aung San Suu Kyi in a 2021 coup.

Frustration has mounted among some members of the 10-country bloc over how to handle Myanmar and its bloody political turmoil and Thailand's latest move will raise fresh questions about the group's unity.

Two sources with knowledge of Sunday's meeting told Reuters that Myanmar's junta-appointed foreign minister had been invited. Myanmar's military spokesman did not respond to phone calls on Friday night.

ASEAN chair Indonesia has declined to attend the proposed meeting, according to three sources. Indonesia's Foreign Ministry told Reuters it "hasn't heard" about the invitation.

Asked about the Thai proposal on a visit to Washington, Singaporean Foreign Minister Vivian Balakrishnan told reporters that since there had been no improvement in the situation in Myanmar, "it would be premature to re-engage with the junta at a summit level or even at a foreign minister level".

The foreign ministry in Thailand declined to comment. Thailand is expected to have a new government by August following an election last month that saw the ruling pro- military coalition trounced by progressive and populist parties.

Myanmar's ruling generals for nearly two years have been barred by ASEAN from its high-level meetings over its failure to honour a 2021 agreement, known as the "5-point consensus", which included calls for an cessation of hostilities, dialogue between all parties and the granting of full humanitarian access.

The government of Thailand - whose current prime minister, Prayuth Chan-ocha, himself first came to power in a army coup - has previously sought to bring Myanmar's military officials back into informal talks with ASEAN counterparts - at times putting it at odds with efforts by Indonesia.

A source in Jakarta said Indonesia's rejection of the invitation included the fact that Thailand's initiative contradicted the recent ASEAN agreement at the May summit.

Foreign Minister Don's letter said the proposed meeting would be "part of the initial steps" of the peace process and cited the summit where "a member nation" made an unequivocal statement that ASEAN should fully re-engage with Myanmar at the leadership level.

"A number of members supported the call and some were willing to consider, there was no explicit dissenting voice," Don said in the letter.

"Should this informal ministerial engagement make substantial positive progress, we would like to suggest that a carpe diem back-to-back meeting of leaders be convened thereafter."

Phil Robertson, deputy Asia director of Human Rights Watch, said the Thai foreign minister had shown "arrogance" by inviting his junta counterpart who other regional neighbours have shunned.

"No wonder ASEAN's efforts have been stymied at every step to resolve the Myanmar crisis," he said.

Thailand's progressive Move Forward Party, which won most seats in the May election, has signalled that if it is able to form a government, it intends to follow a different policy on Myanmar from the current pro-military coalition that was soundly defeated at the polls.

Indonesia last month cited progress in its own behind-the-scenes efforts to engage multiple parties in Myanmar's conflict in a bid to advance a peace process agreed by ASEAN leaders and Myanmar's military in April 2021.

Myanmar has been roiled by violence since the Feb. 1, 2021 coup, with the military battling on multiple fronts to try to crush an armed pro-democracy resistance movement formed in response to the crackdown.

Human rights and some United Nations experts have accused the military of committing widespread atrocities. The junta says it is fighting terrorists who aim to destroy the country.

(Ananda Teresia reported from Jakarta. Additional reporting by Devjyot Ghoshal and Kay Johnson in Bangkok, Stanley Widianto in Jakarta, Simon Lewis in Washington, and Shoon Naing; Writing by Martin Petty and Devjyot Ghoshal, Editing by Angus MacSwan)