The bodies of the two Newcastle University students were found early Wednesday lying in a road in Kuching, capital of the state of Sarawak on Borneo island.
The victims have been identified as Neil Dalton and Aidan Brunger, both 22.
The medical students were on a six-week placement in a hospital in Kuching as part of their studies.
Police have arrested four male suspects, aged between 19 and 30, and confiscated a knife they believe was used in the killings.
"All the four men have admitted to the crime. We are investigating them for murder," Chai Khin Chung, Sarawak's deputy police chief, told AFP by phone.
They could face the death sentence.
Chai said initial investigations indicated the incident started when the two Britons, who had been drinking, began arguing loudly between themselves in a local bar.
The four Malaysian suspects, who had also been drinking, confronted the medical students and told them to be quiet, he added.
"Then one of the British students slapped one of the locals, turned over a table, and walked out," he said.
The locals followed in a car, and one of them attacked the Britons with the knife.
Chai said some of the suspects had prior criminal records.
Malaysia is generally a safe country for foreign visitors but some recent incidents have sullied that image.
Malaysian police in early June found the body of 34-year-old British tourist Gareth Huntley on the resort island of Tioman.
They are yet to announce the cause of death.
Last month, a court sentenced to death a Malaysian shopkeeper for the killing of French tourist Stephanie Foray in May 2011, also on Tioman.