"We are fighting with each other, it is serious gunfire," Kanharith said.
Thailand's Foreign Ministry denied that any Thais had been seized.
The latest fighting comes a day after a Thai soldier lost a leg when he stepped on a landmine in an area claimed by Thailand.
A Thai patrol visited the blast site on Friday morning and encountered 20 Cambodian soldiers.
"After talks between the two sides failed, the Cambodian side started to walk away and turned back to open fire at Thai troops with rifles and RPG rockets, forcing the Thai side to fire back in self-defence," the Thai foreign ministry said in a statement.
There were reports of more fighting in the afternoon, hours after Thai and Cambodian commanders met for talks on the border.
The 11th-century temple was built in the reign of King Suryvarman I, during the 600-year Khmer empire.
Built to honour the Hindu god Shiva, the temple has withstood decades of war.
In 1998, hundreds of Khmer Rouge guerrillas made their final surrender at the temple.
Unesco deemed the temple a World Heritage site for its location, rare architecture, religious function and carved stone ornaments.
The latest gunfight happened after a Thai general described the first incident as a "misunderstanding".
Cambodian officials said Friday's first shootout began after Thai troops crossed into Cambodian territory.
The landmine incident a day earlier had already put Cambodian troops on "high alert" said Thai officials.
Earlier this week Hun Sen, the Cambodian prime minister, had warned Thailand that it would face fighting if its troops crossed their disputed frontier.
But Thailand denies claims that about 100 of its troops had crossed over the frontier.
Hun Sen and Abhisit Vejjajiva, the Thai prime minister, are scheduled to attend a summit between the Association of Southeast Asian Nations (Asean) and key regional partners in the Thai resort of Pattaya next week.
The conflict focuses on an area of land of just over five square kilometres surrounding the temple.
Ownership of the property itself was awarded to Cambodia by an international court in 1962, but ownership of the surrounding land has remained in dispute.
"There is also a lot of very unhelpful political wrangling at the top levels"
Laura Kyle, Al Jazeera
The recent listing of the temple as a UN World Heritage site has revived nationalist tensions in Thailand and Cambodia.
The same area was the scene of several clashes last year, with four soldiers killed in October.
Al Jazeera's Laura Kyle reporting from Phnom Penh said: "Violence peaked last year when the temple became a world heritage site ... there are negotiations taking place to try and diffuse the situation and bring the fighting to a halt.
"But there is also a lot of very unhelpful political wrangling at the top levels," she said.