At least 30 people have been killed and more than 130,000 people displaced in the worst fighting between the Southeast Asian neighbours in 13 years, with both sides saying they have acted in self-defence.
There were clashes early on Saturday, both sides said, in the neighbouring Thai coastal province of Trat and Cambodia's Pursat Province, a new front more than 100km from other conflict points along the long-contested border.
The two 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.
As of Saturday, Thailand said seven soldiers and 13 civilians had been killed in the clashes, while in Cambodia, five soldiers and eight civilians had been killed, Defence Ministry spokesperson Maly Socheata said.
In the Thai border province of Sisaket, a university compound has been converted into temporary accommodation, where a volunteer said more than 5000 people were staying.
Samrong Khamduang said she left her farm, about 10km from the border, when fighting broke out on Thursday. The 51-year-old's husband stayed behind to look after livestock.
"We got so scared with the sound of artillery," she said.
In Kuala Lumpur, Malaysian Prime Minister Anwar Ibrahim, the chair of the ASEAN regional bloc, said he would continue to push a ceasefire proposal.
Cambodia has backed Anwar's plan, while Thailand has said it agreed with it in principle.
"There is still some exchange of fire," Anwar said, according to state news agency Bernama.
He said he had asked his foreign minister "to liaise with the respective foreign ministries and, if possible, I will continue engaging with them myself - at least to halt the fighting".
Thailand's ambassador to the UN 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.
"Thailand urges Cambodia to immediately cease all hostilities and acts of aggression, and resume dialogue in good faith," Cherdchai Chaivaivid told the council in remarks released to the media.
Cambodia's defence ministry said Thailand had launched "a deliberate, unprovoked, and unlawful military attack" on Thursday, and was now mobilising troops and military equipment on the border.
"These deliberate military preparations reveal Thailand's intent to expand its aggression and further violate Cambodia's sovereignty," the ministry said in a statement on Saturday.
Cambodia called for the international community to "condemn Thailand's aggression in the strongest terms" and to prevent an expansion of Thailand's military activities.
Bangkok reiterated it wanted to resolve the dispute bilaterally, telling the Security Council it was "deeply regrettable that Cambodia has deliberately avoided meaningful dialogue and instead sought to internationalise the issue to serve its own political objectives".
Thailand and Cambodia have bickered for decades over the jurisdiction of various un-demarcated points along their 817km land border, with ownership of the ancient Hindu temples Ta Moan Thom and the 11th century Preah Vihear central to the disputes.
Preah Vihear was awarded to Cambodia by the International Court of Justice in 1962, but tension escalated in 2008 after Cambodia attempted to list it as a UNESCO World Heritage site.
That led to skirmishes across several years and at least a dozen deaths.
Cambodia in June said it had asked the court to resolve its disputes with Thailand, which says it has never recognised the court's jurisdiction and prefers a bilateral approach.