The country "agrees in principle to a ceasefire", says Thailand's Deputy Prime Minister Phumtham Wechayachai on X.
Earlier on Saturday evening, US President Donald Trump stated that both parties want an immediate ceasefire and peace, after speaking with the countries' leaders.
"They have agreed to meet immediately and quickly agree on a ceasefire and ultimately peace", Trump wrote on his social media platform Truth Social.
Trump also emphasized that the US is "temporarily" negotiating tariffs with both countries, but will not conclude any new agreements with them if the fighting continues.
Kambodja's UN ambassador Chia Keo said already on Friday that the country wants an immediate ceasefire "unconditionally", after a crisis meeting in the UN Security Council on the conflict.
In total, 13 people, eight civilians and five soldiers, have been confirmed dead in Kambodja in the recent clashes, according to Maly Socheata, spokesperson for Kambodja's defense department. 71 people are said to have been injured.
Thailand reports that six soldiers and 13 civilians, including children, have been killed on the Thai side. 29 soldiers and 30 civilians are said to have been injured.
"Like siblings"
But the population in both countries does not want to be at war with each other.
The relationship used to be good - we were like siblings, says Thai Sai Boonrod to the news agency AFP.
We are neighbors, we want to be friends, is the statement from an anonymous man on the other side of the border.
According to the authorities in Thailand, 138,000 people have fled their homes in the border areas with Kambodja. On the Kambodjan side, 35,000 people have been evacuated from the border, according to the country's defense department.
Broke out on Thursday
The clashes between the countries broke out on Thursday night - after five Thai soldiers were injured in a mine explosion the day before.
The UN Security Council has not made any statement after the meeting. But a diplomatic source tells AP that all 15 member countries are urging de-escalation and a peaceful solution.
Malaysia, which is currently the chairman of the Southeast Asian association Asean, has offered to mediate.
Accuse each other
The parties have, among other things, fired artillery and rockets at each other. Thailand has also carried out air raids.
Both countries accuse each other of having shot first, in the bloodiest fighting between the parties in a decade. In comparison, 28 people were killed in clashes between the countries in 2008-2011.
Sporadic acts of violence have occurred over the past 15 years. This year, the relationship between the countries has deteriorated significantly since May, when a Kambodjan soldier was shot dead at the border.