And Cambodia has indicated its troops will not move until Thailand begins a withdrawal.
Several thousand Thai and Cambodian troops have been staking out the area, which surrounds the Preah Vihear temple, for the past few weeks.
Our South East Asia correspondent, Karen Percy, says on Monday, the foreign ministers of both countries agreed to pursue a troop withdrawal.
Tensions flared earlier this month when Cambodia succeeded in getting World Heritage listing for the Hindu temple, which is surrounded by disputed territory.
Thailand had initially supported the bid but was forced to withdraw after a public outcry.
Thailand's cabinet has discussed the issue, with the government saying it will talk to the country's senior military leaders about when and how to scale back the military presence.
The ruins of the Preah Vihear temple, which sits on a mountaintop overlooking the jungle, belong to Cambodia, but the most practical entrance begins at the foot of a mountain in Thailand.
Both sides claim some of the surrounding territory and say a full resolution of the decades-long dispute is likely to involve protracted negotiations.
The latest conflict has inflamed nationalist sentiment in both countries.