Thailand's acting prime minister, Phumtham Wechayachai, thanked Trump and said Thailand "agrees in principle to have a ceasefire in place" but "would like to see sincere intention from the Cambodian side".
Trump said he had spoken to Cambodian Prime Minister Hun Manet and Phumtham and warned them that he would not make trade deals with either if the border conflict continued.
"Both Parties are looking for an immediate Ceasefire and Peace," Trump wrote as he gave a blow-by-blow account of his diplomatic efforts.
"When all is done, and Peace is at hand, I look forward to concluding our Trading Agreements with both!"
Phumtham also said he had asked Trump "to convey to the Cambodian side that Thailand wants to convene a bilateral dialogue as soon as possible to bring forth measures and procedures for the ceasefire and the eventual peaceful resolution of the conflict".
More than 30 people have been killed and more than 130,000 people displaced in the worst fighting between the Southeast Asian neighbours in 13 years.
Before Trump spoke to the two leaders, Thai-Cambodian border clashes persisted into a third day and new flashpoints emerged.
He offered no details on the ceasefire negotiations he said Thailand and Cambodia had agreed to hold.
The White House did not immediately respond to questions on the timing and venue for talks and the Thai and Cambodian embassies in Washington also did not immediately respond.
There were clashes early on Saturday, both sides said, in the Thai coastal province of Trat and Cambodia's Pursat Province, a new front more than 100 kilometres from other conflict points along the long-contested border.
The countries have faced off since the killing of a Cambodian soldier late in May during a brief skirmish.
Troops on both sides of the border were reinforced amid a full-blown diplomatic crisis that brought Thailand's fragile coalition government to the brink of collapse.
Thailand's UN ambassador told a Security Council meeting on Friday that soldiers had been injured by newly planted land mines in Thai territory on two occasions since mid-July, claims Cambodia has strongly denied, and said Cambodia had then launched attacks on Thursday morning.
On Saturday, Cambodia accused Thailand of "a deliberate, unprovoked, and unlawful military attack" and said "military preparations reveal Thailand's intent to expand its aggression and further violate Cambodia's sovereignty".
It called for the international community to condemn Thailand's "aggression" and prevent an expansion of its military activities, while Bangkok says it wants to resolve the dispute bilaterally.
Southeast Asia expert Gregory Poling of Washington's Centre for Strategic and International Studies was cautious about Trump's intervention speeding up a ceasefire.
"Neither Cambodia nor Thailand -- or their publics -- will appreciate the threat to weaponise trade to make it happen. And if they do reach a ceasefire and either or both still don't get a trade deal before August 1, they are likely to view it as a US betrayal."
Thailand and Cambodia have bickered for decades over undemarcated points along their 817-kilometre land border, with ownership of the ancient Hindu temples Ta Moan Thom and the 11th century Preah Vihear central to the disputes.
