But with Thailand steadfastly rejecting any outside mediation it is unclear what the other eight ministers from the 10-member Association of Southeast Asian Nations (ASEAN) can do to end the row.
"ASEAN foreign ministers are gathering in Jakarta for an Indonesia-facilitated urgent meeting to discuss possible solutions to the recent border conflict," the ASEAN secretariat said in a statement.
The conflict, which has seen exchanges of small arms, mortars and artillery, centres on the 900-year-old Hindu temple of Preah Vihear and its surrounding area, which is claimed by both sides.
Thailand and Cambodia have each accused the other of starting the clashes, which have killed at least 10 people and displaced thousands on both sides of the frontier.
Phnom Penh has called for third-party mediation to help achieve a permanent ceasefire but Bangkok insists the dispute should be resolved bilaterally, and has urged Cambodia to return to the negotiating table.
Tuesday's talks in Jakarta will be the first meeting between Cambodian Foreign Minister Hor Namhong and his Thai counterpart, Kasit Piromya, since they met behind closed doors at the UN Security Council a week ago.
The conflict is a test for ASEAN, which lacks any strong conflict resolution framework, and for founding member Indonesia which took over the chair of the block at the start of the year.
Indonesian Foreign Minister Marty Natalegawa attended the meeting in New York and has offered to mediate between the two sides.
"There is a strong desire to settle differences through peaceful means as agreed by all ASEAN member states under the Treaty of Amity and Cooperation in Southeast Asia," he said, according to the ASEAN statement.
The minister's spokesman, Michael Tene, said the talks would explore ways ASEAN can "facilitate and create conducive conditions for the two countries to carry out negotiations".
"The UN supports ASEAN's efforts to facilitate a peaceful resolution to the conflict and the meeting today will discuss the modalities," he told AFP ahead of the ministerial talks in Jakarta.
Asked whether Thailand would agree to outside mediation, he said: "Let's just say now that both countries have accepted facilitation from Indonesia."
Ties between the neighbours have been strained since Preah Vihear was granted UN World Heritage status in July 2008.
The World Court ruled in 1962 that the temple belonged to Cambodia, but both countries claim ownership of a 1.8-square-mile (4.6-square-kilometre) surrounding area.