Cambodia has called for an "immediate" ceasefire with Thailand, as the two countries have seen more than 30 people killed, including civilians, in the ongoing border clashes.

Cambodia's ambassador to the UN, Chhea Keo, said his country asked for a truce "unconditionally", adding that Phnom Penh also wanted a "peaceful solution of the dispute".

Thailand's foreign minister Maris Sangiampongsa said on Saturday that Cambodia needed to show "genuine sincerity in ending the conflict" for ceasefire talks to proceed.

At least 32 people - soldiers and civilians - have been killed and nearly 200,000 displaced in the two Southeast Asian countries, who accuse each other of firing the first shots on Thursday.

Fighting continued for a third day on Saturday. Thailand's military said the Cambodians launched attacks in a new area near the coast in the south, but were pushed back by the navy.

Earlier, Thailand reported fighting in its Surin, Ubon Ratchathani and Srisaket provinces, along the border with Cambodia. It has declared martial law in eight districts bordering Cambodia.

Officials in Bangkok said 19 people - 13 civilians and six soldiers - have been killed in the country since Thursday.

Nearly 140,000 people have been evacuated, Thai officials added.

Cambodia's defence ministry has reported 13 killed - eight civilians and five soldiers.

It said more than 35,000 people have fled their homes.

Thailand's acting Prime Minister Phumtham Wechayachai on Friday warned that the clashes could "move towards war".

He said the fighting now included heavy weapons and had spread to 12 locations along the border.

Thailand also accused Cambodia of firing into civilian areas and evacuated all villages deemed to be within the radius of its rockets.

Cambodia, for its part, accused Thailand of using cluster munitions. Cluster munitions are banned in much of the world because of their indiscriminate effect on civilian populations. Thailand has not responded to the allegations.

Meanwhile, Thailand's foreign minister told the Reuters news agency there was "no need" for third-party mediation in the conflict, even as global leaders appealed for an immediate ceasefire.

Malaysian Prime Minister Anwar Ibrahim, who chairs the Association of South East Asian Nations (Asean), had earlier offered to facilitate talks between the two countries.

The US also called for an "immediate cessation of hostilities, protection of civilians and a peaceful resolution of the conflict".

Thailand says the clashes began with Cambodia's military deploying drones to conduct surveillance of Thai troops near the border.

Cambodia says Thai soldiers initiated the conflict when they violated a prior agreement by advancing on a Khmer-Hindu temple near the border.

The dispute between the two countries dates back to more than 100 years ago, when the borders of the two nations were drawn after the French occupation of Cambodia.

There have been sporadic clashes over the years which saw soldiers and civilians killed on both sides.

The latest tensions ramped up in May after a Cambodian soldier was killed in a clash, plunging bilateral ties to their lowest point in more than a decade.