"Smoke is observed with medium pressure with a thick grey colour and with a maximum height of about 700m above the peak," local authorities said.
Locals are being urged to remain calm and not to panic.
Indonesia's National Disaster Management Agency said the eruption remained small so far but the volcano was emitting a thick grey ash cloud blowing to the east and southeast.
There has been no change to an evacuation zone around the volcano, which extends between 6 to 7.5km from the summit.
More than 140,000 people fled homes around the crater last month for fear the volcano would erupt.
Nearly 1600 people died when Agung last erupted in 1963, but officials said that the rumblings did not pose an immediate threat to those living in its shadow.
Agung has been rumbling intermittently since August.
The alert level remains at three after it was downgraded from the maximum level of four on October 29.
"At this point this is very, very small," tweeted New Zealand volcanologist Dr Janine Krippner.
"Right now this is not a serious eruption but of course this can change.
"Time to make sure you are prepared and keep an eye on official Agung information."
Bali's Ngurah Rai International Airport remains open.
Officials estimated concerns about an eruption over the past few months had cost Bali at least $110 million in lost tourism and productivity as many local residents moved to shelters.
Indonesia is home to around 130 volcanoes due to its position on the "Ring of Fire", a belt of tectonic plate boundaries circling the Pacific Ocean where frequent seismic activity occurs. In 2010 Mt Merapi - considered one of the most active and dangerous volcanoes in the world - erupted, killing some more than 300 people and forcing 280,000 people to flee.
Mt Sinabung on Sumatra island - which is currently also at its highest alert level - has been active since 2013.
