The head of the Kerobokan prison, Tony Nainggolan, named the four as Shaun Edward Davidson from Australia, Dimitar Nikolov Illiev from Bulgaria, Sayed Muhammad from India, and Tee Kok King from Malaysia. "Maybe we should change the law", he said.
Nainggolan believes they spent more than a week building the tunnel. "We found two buckets, some towels and sandals near it (the tunnel entrance)", he said.
In May, about 200 prisoners broke out of an overcrowded jail in Sumatra island after being let out of cells for Friday prayers.
"We allege that they escape through the underground hole", he said.
Some reports said it was an existing tunnel used for water drainage.
The men include Australian Shaun Davidson, who was locked up for using a fraudulent travel document and only had two months left to serve of his one-year sentence. He later arrived in Indonesia on a one-month tourist visa.
Bali authorities are launching increased checks at the airport, port and bus terminals to apprehend the prisoners.
The four men were serving sentences for different crimes, from immigration rules violation to drug crimes, Widjaja said. A 40cm-diameter tunnel was found behind the jail's clinic, close to a guard tower. As Reuters notes, prison escapes are fairly common in the Southeast Asian country.
The prison's governor confirmed he fled the Indonesian prison on Monday morning, according to 9 News.