Secretary of State Marco Rubio said American diplomats were in Malaysia on Monday to help broker a cease-fire between Cambodia and Thailand, which are engaged in a deadly conflict along the countries’ border.

The leaders of Cambodia and Thailand agreed on Sunday to begin cease-fire talks in Malaysia’s capital, Kuala Lumpur. President Trump said he had spoken to both leaders and that U.S. officials would not negotiate trade deals with either country unless the fighting stopped.

At least 35 people have been killed since the combat began on Thursday, and hundreds of thousands of civilians have fled the border areas where it is taking place. Fighting apparently continued early Monday, with the sound of explosions heard near the border before dawn.

The conflict flared after two months of tension over contested territory. As of Monday, the death toll exceeded that from the last outbreak of deadly battles in the region, between 2008 and 2011, during which 34 people were killed, according to an academic paper.

Some Cambodians have fled to the homes of family members and friends here in Siem Reap, the site of the ancient Angkor Wat temple complex. Siem Reap has been untouched by the violence, but at Hindu and Buddhist shrines around Angkor Wat, people have held ceremonies to pray for a quick resolution to the war. On Sunday, after Mr. Trump announced his diplomatic intervention, residents began talking in hopeful terms of an American role in prodding the warring governments toward a cease-fire.