Thailand said one of its soldiers was wounded in the latest incident on the border on Tuesday. The two armies accused each other of using hand grenades.
Bangkok called on its neighbour to return to the table for bilateral talks to settle the dispute, which centres on the 900-year-old Preah Vihear temple on the border of the two countries.
Talks erupted into four days of armed clashes that left at least 10 people dead earlier this month.
"When the international community thinks the problem should be solved through negotiation, Cambodia has no reason to refuse. They should return to the talks," Thai Prime Minister Abhisit Vejjajiva said.
But Phnom Penh rejected the call, insisting on the need for third-party mediation.
"Bilateral negotiations do not work," said Cambodian Foreign Ministry spokesperson Koy Kuong.
"All negotiations must always have the participation of a third party," he said. "What Cambodia wants is a permanent ceasefire. This is the most important issue."
The two sides are at odds over a border area surrounding the 11th century Hindu temple, which is situated on a clifftop in Cambodia but whose main entrance is in Thailand.
UN Security Council President Maria Luiwa Ribeiro Viotti called for "maximum restraint" in the standoff as they work toward a permanent ceasefire.
But just hours later, the two countries' armies were accusing each other about the latest border incident.
While Cambodia won support for its calls for outside mediation to help end the standoff, the council did not endorse its request to deploy UN peacekeepers into the contested area.
Thai Foreign Minister Kasit Piromya, however, said there was no need for UN peacekeepers at all.
Kasit said he had not met his Cambodian counterpart one-on-one in New York.
The two will have the opportunity to do so during a meeting of foreign ministers from the Association of Southeast Asian Nations (Asean) in Jakarta on 22 February.