The latest alert - a red warning - means an eruption is forecast to be "imminent" after nearby locals spotted volcanic ash rain.
Ash fall was reported in the villages of North Duda, East Duda, Pempetan, Besakih, Sidemen, Tirta Abang, Sebudi, Bhuana Amerta in Klungkung and in some villages in Gianyar.
Bali is a major tourist destination, although the main resorts of Kuta and Seminyak are about 70km from the volcano.
Bali is an important tourist centre and the global airport of Denpasar, the capital of the island, is operating normally for the moment, even if some airlines made a decision to cancel their flights.
According to the Volcanic Observatory Notice for Aviation (VONA) system, winds carried the ash in an eastern and southeastern direction.
Travellers to and from the region are being urged to contact their airline or travel agent to find out the status of their flight. It is still gushing and the dark grey clouds are moving toward the neighbouring island of Lombok, a direction that is away from Bali's airport, where almost all scheduled domestic and worldwide flights were continuing Sunday.
The information director of Indonesia's Disaster Mitigation Agency tweeted that volcanic ash rain had fallen on the Lombok city of Mataram.
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Worldwide airlines including Jetstar and Qantas have cancelled flights to and from Bali after the second eruption of Mt Agung in a week, even though Indonesia's disaster management authorities say it's safe to fly to the island.
Magma - molten rock - has now been detected close to the volcano's surface, said officials and volcanologists.
The danger zone around Agung was also reduced from a radius of 9 to 12km from the peak in different areas, to a radius of 6 to 7.5km. Suantika said Agung could spew ash for at least a month but did not expect a major eruption.
About 25,000 people are thought to be in shelters while more than 140,000 people fled earlier this year.
According to official estimates, the holiday island lost tens of millions in tourism and productivity during the major evacuation.
Indonesia sits on the "Pacific Ring of Fire" and has more than 120 active volcanoes.
There are fears the volcano could erupt for the first time since 1963, when almost 1,600 people died.
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