All six, who were of Vietnamese descent, checked into Bangkok's Grand Hyatt Erawan hotel at two separate times after arriving on Saturday and Sunday, police official Thiti Saengsawang told reporters.
Two of the group were carrying US passports.
The group - three men and three women - checked into different rooms but their bodies were found in one room, which did not show any signs of struggle, he said.
"This was not self harm, but someone caused the deaths," said Thiti, adding that police were looking for a seventh person connected with the group.
"We are tracing every step since they got off the plane."
Police officers found the bodies after a call from the hotel staff about 5.30pm (local time) reporting that there had been deaths, the Thai police said in a statement.
Thai prime minister Srettha Thavisin, who visited the hotel late on Tuesday with senior police officials, ordered a swift investigation on the matter, the government said in a statement.
"The prime minister has ordered all agencies to urgently take action to avoid impact on tourism," it said.
The US State Department was "closely monitoring the situation and (we) stand ready to provide consular assistance," a spokesperson said, referring questions on the circumstances of the deaths to local authorities.
The Vietnamese embassy in Bangkok did not respond to calls from Reuters.
The Grand Hyatt Erawan, which has over 350 rooms and is located in a popular tourist district in the Thai capital known for luxury shopping and restaurants, also did not immediately respond to calls or an email seeking comment.
Tourism serves as a key driver for Southeast Asia's second-largest economy, with the government expecting 35 million foreign arrivals this year after 28 million visited the country in 2023.
The tourism sector was shaken in October by a shooting spree at a luxury shopping mall close to the Hyatt in which two foreigners were killed, prompting government measures to improve confidence, including ramping up security at popular locations.
To woo more visitors, the government has offered longer visa stay periods and waivers for several nationalities.
