Prime Minister Anutin Charnvirakul posted on Facebook that the Southeast Asian nation would "continue to perform military actions until we feel no more harm and threats to our land and people".
Trump, who brokered a ceasefire in the long-running border dispute in October, spoke to Anutin and Cambodian premier Hun Manet on Friday, and said they had agreed to "cease all shooting".
Neither of them mentioned any agreement in statements after their calls with Trump, and Anutin said there was no ceasefire.
"I want to make it clear. Our actions this morning already spoke," Anutin said on Saturday.
The White House did not immediately respond to a request for comment on the continued fighting.
Hun Manet, in a statement on Saturday on Facebook, said Cambodia continued to seek a peaceful resolution of disputes in line with the October agreement.
Since Monday, Cambodia and Thailand have been exchanging heavy-weapons fire at multiple points along the 800km border, in some of the heaviest fighting since the five-day clash in July.
Trump halted that fighting, the worst in recent memory, with calls to both leaders.
Trump, who has repeatedly said he deserves the Nobel Peace Prize, has been keen to intervene again to rescue the truce.
Thailand suspended it in November after a Thai soldier was maimed by a landmine, one of many that Bangkok says were newly laid by Cambodia.
Cambodia, which nominated Trump for the peace prize in August, rejects the landmine allegations.
On Saturday, a Thai defence ministry spokesman, Rear Admiral Surasant Kongsiri, told a media conference that clashes had taken place across seven border provinces and Cambodia had fired heavy weapons, "making it necessary for Thailand to retaliate".
Cambodia's information ministry said Thai forces had struck bridges and buildings overnight and fired artillery from a naval vessel.
Thai leader Anutin dismissed comments by Trump that a "roadside bomb" that wounded Thai soldiers was accidental, saying the incident was "definitely not a roadside accident".
Cambodia's Hun Manet said he had asked the US and Malaysia, which has been a mediator in peace talks, to use their intelligence gathering capabilities to "verify which side fired first" in the latest round of fighting.
