Hun Sen, who had previously accused Thailand of intrusion into the sanctuary of Ta Kwai in a disputed border area, said in a letter to Somchai that the countries should end the conflict amicably in a spirit of solidarity and good neighbourliness.
The Cambodian premier said his government was willing to cooperate with Thailand for the sake of good relations and mutual benefit.
Cambodia and Thailand have locked horns over Hindu temples - regarded by Phnom Penh as Khmer sanctuaries - along the border since June when Phnom Penh proposed to list the 11th-century Hindu temple of Preah Vihear as a World Heritage site.
The then Thai government was forced by street protests and the parliamentary opposition to withdraw its support for the application, due to fears over a loss of territory. Both countries deployed large numbers of troops into the area.
A series of ministerial meetings tried to negotiate the redeployment of the troops, while Phnom Penh piled on the pressure by accusing the government of sending Thai troops to occupy other Hindu temples, at Ta Muen Thom and Ta Kwai. Thailand argues that the temples belong to the Kingdom and are part of Surin province.
Hun Sen said in his letter of congratulation that Cambodia was confident the new Thai prime minister could help to fix sour bilateral relations and resolve the border problems peacefully.