Thailand and Cambodia have agreed to an "immediate and unconditional ceasefire" after five days of fighting at their border killed at least 33 people and displaced tens of thousands.

"This is a vital first step to a de-escalation and a restoration of peace and security," said Malaysian Prime Minister Anwar Ibrahim, flanked by his Thai and Cambodian counterparts, as he announced that hostilities would end at midnight.

Thailand initially rebuffed his offer to mediate but agreed after US President Donald Trump said tariff negotiations would not proceed until "fighting STOPS".

Tensions over the century-old border dispute had ramped up in May after a Cambodian soldier was killed in a clash.

Thailand imposed restrictions on citizens and tourists heading into Cambodia via land, while Cambodia banned some imports from Thailand, including fruits, power and internet services. Local Cambodian outlets reported that hundreds of thousands of workers had returned from Thailand since May.

The situation escalated last week, after a Thai soldier lost his leg in a landmine explosion. Thailand closed some of its border crossings with Cambodia, expelled their ambassador and recalled its own.

Both sides exchanged gunfire early last Thursday, with each claiming the other had triggered the conflict.

Many of the casualties on the Thai side have been civilians in villages hit by rockets, according to Thailand's army. Cambodia said 13 people had been killed so far on its side, including eight civilians.

Shells and rockets continued to land in both countries even as the peace talks were under way in Kuala Lumpur on Monday.

Anwar said Malaysia and other members of the regional bloc, Association of South East Asian Nations, or Asean, were on hand to help monitor the ceasefire.

Both sides will need to agree to pull their armies, which have now been greatly reinforced, back from the border, and to accept some kind of independent monitoring, to prevent further clashes.

Cambodia's Prime Minister Hun Manet described it as a very good meeting that he hoped would immediately stop the fighting. Cambodia has been pushing for a ceasefire since Friday, as its outgunned forces have been driven back by the Thai military.

Acting Thai PM Phumtham Wechayachai spoke briefly, promising to honour the ceasefire.

The situation on the front lines, which are accessible only to the two armies, is still unclear.

Thailand claims to have taken control of a number of Cambodian-held hills, and kept up a sustained artillery barrage from its much larger arsenal of heavy guns, as well as hitting Cambodian positions from the air.

The Thai government was reluctant to join peace talks, saying that a ceasefire could only follow a dialogue between the two countries and "sincere intentions" from Cambodia, by which it meant an end to the rocket barrages which have killed at least 14 Thai civilians.

While Malaysia brokered the talks, as much credit probably belongs in Washington, with President Trump. His ultimatum on Saturday night, threatening to stop all negotiations on reducing US tariffs unless the two countries agreed to stop fighting, was almost certainly what forced them to accept the ceasefire.

Both are heavily dependent on exports to the US and both face a 36% tariff on exports without a deal. That would put their manufacturers at a big disadvantage to those in neighbouring countries like Vietnam and Indonesia, which have already done deals to reduce their tariffs to 20% or less.

But maintaining the ceasefire will be hard, given that there is now deep mistrust between the two armies, and a lot of powerful nationalist sentiments have been stirred up.

Thailand is especially aggrieved by the sudden use of multiple rocket launchers on Thursday that caused most of the civilian casualties, and dramatically escalated what until then had been small-scale skirmishes between their soldiers.

Older evacuees near the Thai border who had lived through bombardments during the Cambodian Civil War of the 1980s told the BBC last week that this is the worst they had experienced.

The Thai military had said on Sunday that nearly 140,000 civilians had been evacuated to shelters across seven provinces.

In Cambodia, where the press is severely restricted, the pro-state Khmer Times quoted a defence ministry spokesperson who said about 135,000 people along the border were relocated on Sunday.

A 75-year-old Cambodian woman who was evacuated to a shelter told the BBC earlier on Monday that she still did not feel safe because she could hear Thai drones fly over the tents.

She said she wanted to "see the war stop this evening".