The volcano, located some 50 miles from Kuta, a popular tourist destination, has been rumbling since August.
Mount Agung last eruption, in 1963, killed over 1,000 people.
According to Indonesia's disaster mitigation agency, the number of people fleeing their homes has tripled since Friday.
"The evacuation process is ongoing and we expect the number of evacuees to continue to rise," agency spokesman Sutopo Purwo Nugroho told AFP news.
Officials are urging people to stay at least 6 miles from the volcano's crater.
Locals are growing increasingly concerned.
"I am actually very worried to leave, I left my cows and pigs at home because we were ordered to vacate our village immediately," villager Nyoman Asih told AFP.
The international airport of the island's capital, Denpasar, is prepared to close if necessary although currently no changes have been made to flight schedules. The airport has also proactively organized buses and trains to transport passengers to neighboring provinces in case of eruption, Al-Jazeera reported.
The Indonesian Centre for Volcanology and Geological Hazard Mitigation said that although fewer tremors took place on Sunday, those that did take place were stronger than previous quakes.
"The mountain has not erupted until now, the earthquake happens less frequently but the magnitude is getting stronger," Gede Suantika, a senior volcanologist at the agency, said.